I get the opposite situation, I use a heavy 777 PMDG for example and I get a small push back! How the weight determines the vehicle then?
The weight that count's, is the actual one at the moment you called GSX for the first time, and opened its menu, which will start the vehicle creation/selection around the parking.
This means, if you did this with a fairly light airplane, GSX selected the smaller truck (even if it's small, it can push up to 175.000 lbs. ), but if you loaded the airplane using the PMDG menus and/or used any kind of progressive loading method, GSX won't "update" the vehicles you called, just because the plane changed its weight in the meantime.
Just be sure the weight is final, before you call GSX.
And, there might be a parking size restriction too, since larger vehicles are prevented to appear in smaller parkings. So, even if you "forced" GSX to accept a 777 in a parking the original scenery developer set too small in the AFCAD, even if GSX will allow you to be serviced there, it will still use the original size to select the vehicles, because the whole point of the size restriction, is to prevent larger pushback truck to appear in spaces that might not big enough to maneuver.