I believe that all depends on whether your design spectrum is in normalised or denormalised form. For instance if the vertical axis of the spectrum is Se/g then your scale factor would be the gravitational constant g.
The seismic base shear (V) in equivalent static lateral force method is obtained by similar equation in nearly all codes as follows:
V = C (or Cs) * Weff
Which in UBC97 C = A*B*I/R
A depends to seismicity level of region, B depends to fundamental period and site classification (obtained from spectrum), I is important factor of building and R is response modification factor.
and in ASCE-07, Cs = Sds/(R/Ie)
parameters are nearly same as UBC-97.
Now, if we define our spectrum to software, there will be no need to introduce the parameter which depends to the spectrum, i.e. B in UBC97 and Sds in ASCE-07.
and about gravity acceleration (g), if you use equivalent static method there is no need to multiple it, but if you define spectrum it must be considered.
*******NOTE*****
be careful about the software that you are using. SAP2000 and ETABS have an ability named as "Mass Source" which enables automatically calculating masses from defined weights. for example OpenSEES has no function.
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Also, codes have another regulation on this method and that's scaling obtained base-shear to 90% (in regular buildings) and to same (in non regular buildings) value of base-shear from equivalent static method. Therefore, you must first analyze with aforementioned scaling factor and then modify it. It is obvious that results of second analysis must be employed.
Just to add to what Reza Allahvirdizadeh already said, it is very important to be consistent on where and how you scale the spectrum. In SAP2000 the scaling can already be done in the spectrum input, in the load definition and/or in the load combination by introducing coefficients. It is very important to check in a first instance if the weight and base shear correspond to the magnitude that you expected.