It essentially depends on what you are looking at:

Problem 1. The thickness of the boundary layer on a flat plate with zero pressure gradient (constant edge velocity Ue=Uo), at some point X measured from the plates leading edge.

Problem 2. Or, the evolution of boundary layer layer thickness on a flat plate subject to a favorable pressure gradient (edge velocity Ue increases with X) as you move downstream along the flat plate.

// Problem 1:

When considering problem 1, it is indeed the case that the boundary layer thickness will decrease when you increase the speed of the outer flow (edge velocity), all other parameters kept equal and as noted in the previous replies. Dimensional analysis gives food insight into the problem by providing order of magnitude estimates (wikipedia is your friend, but Schlichting or White are far more dependable on this topic):

For Laminar Boundary Layers: delta99 = 5*sqrt(nu*x /Uo)

For Turbulent Boundary Layers: delta99 = 0.37x/Re_x^(1/5) with Re_x=U0o*x/nu

// Problem 2:

Now, when you look at problem 2, things are a bit more complicated: typically, the boundary layer grows as you move downstream along the flat plate, even though it grows slower in favorable pressure gradients (increasing Ue with X) than in adverse pressure gradients (decreasing Ue with X). Still, these are rules of thumb for what happens in the absence of complicated phenomena (like transition, relaminarization, laminar recirculation bubbles, separation and reattachment). In those cases, you have no issue but to compute the flow, either with integral boundary layer methods, finite difference boundary layer solvers or full blown Navier Stokes solvers.

// Why boundary layer thickness?

That being said, it might be wise to consider why you are interested in boundary layer thickness (delta_99) at all. In fact, delta_99 is a fairly ill defined quantity, hard to measure and with little practical application. Boundary layers are far better described using so called higher order moments, such displacement thickness (delta*=delta1), momentum thickness (theta=delta2) and energy thickness (delta**=delta3). The ratio's between these thicknesses give useful information on the shape of the velocity profile, usually expressed as shape factors (H=H12=delta1/delta2  or H*=H32=delta3/delta2). These quantities can be combined to construct of correlations for skin-friction (tau_w), related with friction drag, whereas delta* can be used to estimate the effect of the boundary layer on the outer flow to infer pressure drag (via the Lighthill interaction law).

No, it decreases.

https://en.wikipedia.org/wiki/Boundary_layer_thickness

There is no doubt that the BL thickness will decrease, as the free stream velocity proportional inversely with it. (d ~ 1/u).

It essentially depends on what you are looking at:

Problem 1. The thickness of the boundary layer on a flat plate with zero pressure gradient (constant edge velocity Ue=Uo), at some point X measured from the plates leading edge.

Problem 2. Or, the evolution of boundary layer layer thickness on a flat plate subject to a favorable pressure gradient (edge velocity Ue increases with X) as you move downstream along the flat plate.

// Problem 1:

When considering problem 1, it is indeed the case that the boundary layer thickness will decrease when you increase the speed of the outer flow (edge velocity), all other parameters kept equal and as noted in the previous replies. Dimensional analysis gives food insight into the problem by providing order of magnitude estimates (wikipedia is your friend, but Schlichting or White are far more dependable on this topic):

For Laminar Boundary Layers: delta99 = 5*sqrt(nu*x /Uo)

For Turbulent Boundary Layers: delta99 = 0.37x/Re_x^(1/5) with Re_x=U0o*x/nu

// Problem 2:

Now, when you look at problem 2, things are a bit more complicated: typically, the boundary layer grows as you move downstream along the flat plate, even though it grows slower in favorable pressure gradients (increasing Ue with X) than in adverse pressure gradients (decreasing Ue with X). Still, these are rules of thumb for what happens in the absence of complicated phenomena (like transition, relaminarization, laminar recirculation bubbles, separation and reattachment). In those cases, you have no issue but to compute the flow, either with integral boundary layer methods, finite difference boundary layer solvers or full blown Navier Stokes solvers.

// Why boundary layer thickness?

That being said, it might be wise to consider why you are interested in boundary layer thickness (delta_99) at all. In fact, delta_99 is a fairly ill defined quantity, hard to measure and with little practical application. Boundary layers are far better described using so called higher order moments, such displacement thickness (delta*=delta1), momentum thickness (theta=delta2) and energy thickness (delta**=delta3). The ratio's between these thicknesses give useful information on the shape of the velocity profile, usually expressed as shape factors (H=H12=delta1/delta2  or H*=H32=delta3/delta2). These quantities can be combined to construct of correlations for skin-friction (tau_w), related with friction drag, whereas delta* can be used to estimate the effect of the boundary layer on the outer flow to infer pressure drag (via the Lighthill interaction law).

Thickness will decrease....B/L growth depends on surface too.

Gael gave you a sound answer.

Please remember that, everything else remaining constant, increasing the velocity of the fluid means increasing the flow Reynolds number.

Now, since the Reynolds number can be regarded as the ratio between inertia forces and viscous ones, its increasing means a lower importance of viscous effects and therefore a less extended zone of velocity variation.

Good luck for your work and regards

Calculate Reynolds number (based on the reference length) and use formulae (laminar or turbulent) to know t boundary layer thickness (2D, axisymmetric, wedge etc) and in-compressible or compressible.  Please get detail

Boundary-Layer Theory by H. Schlichting (Deceased),  McGraw-Hill New York

It will decrease. As with incresing fluid velocity the Re(with some ref. length scale) will increase. Thus the inertial to viscous force raitio will increase. Consequently the viscous effect imposed on fluid flow due to the effect of the surface (no slip BC) over which flow is taking place will be confined to smaller BL thickness.   

Obviously by increasing velocity on flat plate boundary layer decreases. 

The critical boundary layer thickness is zc = 3(vt)^0.5, where v is the kinematic viscosity and t is the time of travel t = x/U.  Thus, zc is inversely proportional to U^0.5.  Hence, increasing the velocity will reduce the boundary layer thickness.  YOu can read my paper on Boundary Layer Theory: wave or Particle?  https://www.researchgate.net/publication/265596533_THEORY_OF_BOUNDARY_LAYER_INSTABILITY_PARTICLE_OR_WAVE

Conference Paper THEORY OF BOUNDARY LAYER INSTABILITY: PARTICLE OR WAVE?

The 2014 edition of Boundary-Layer Theory is authored by H. Schlichting and K. Gersten, who is still alive, and is published by Springer.

Certainly, the momentum boundary layer thickness decreases with the increase of velocity of the fluid, resulting in the downfall of its friction with the surface. One can refer to our paper published in 2016.

There are many books explain the BL behaviours. BL thickness increase with velocity decrease.

It is quite evident that as velocity increases boundary layer decreases. The example may be taken for a fluid flow on a flat plate. As the velocity gets increased it dominates the obstruction on the plate.

When you will increase the free stream velocity ,you will increase the Reynolds number which is ( velocity*density*reference length)/viscosity

Reynolds number is the ratio of inertia force by viscous force. It basically shows how momentum exchange is in between the flow. greater the Reynolds number. greater is the inertia or less is the viscosity, for either of this case we get a small boundary layer.

Whatever be the velocity profile we will always get boundary layer thickness inversely proportional to Reynolds no (from von karman momentum integral equation). As we are increasing Reynolds no by increasing velocity we will get smaller boundary layer.