2.001 (the people say it is 2.0023) is not reported it is a defined with a relativity adjustment...the higher value of g is an indication that your magnetic field is shielded by something in your system and felt less strongly than produced by your magnet (or in the case of g
There are many things that affect the g tensor, usually spin orbit coupling. "Electron Paramagnetic Resonance of Transition Ions", Abragam and Bleaney is a good reference for more information.
the magnetic field vector of a "free" electron (of Larmor precession ) is always antiparallel to its spin, i. e. spin-orbit coupling, but in metals we have more than one "free" electron that already without external magnetic field are aligned in such a way that their total energy is at minimum (those minimums are separated by energy barriers, so external force can transfer your system from one local minimum to another).
In general, this is spin-orbit coupling. In terms of chemistry, a positive deviation from free electron g-value, it indicates a d-orbital contribution from d > 5 ions, e.g. Fe3+ d5 ion. I refer you to text book "Electron Paramagnetic Resonance of Transition Ions" by A. Abragam and B. Bleaney.