I was being too literal, I guess. I don't think of the waist straps as a belt because they don't actually go all the way around. It's two separate straps that attach to either side of the frame, and snap in the front.
Now that I'm looking at it correctly, though, that is pretty funny when you see it side by side.
Could just be their posture. Of they loosened / tightened it in the elevator.
I think the position of the waist straps fluctuated differently as they digested their Chinese food.
Venkman ate slower, Stantz was going so fast he barely chewed his food.
So Ray's food was making his belly bulge first, in the lobby. By the time they got up on twelve, Peter's slower digestion was making his belly bulge, while Ray had already needed to cinch back in.
Ahem... From a certain point of view.
Putting aside the jokes and pretending it wasn't a simple continuity error, let's over-think this a little. I find the straps to be perfectly in character for both of them.
After getting out of the Ecto-1, Ray is so eager to rush in and get started he doesn't appropriately tighten up the belt. He just marches in looking sloppy. Peter, on the other hand, is more concerned with making a grand entrance and looking sharp, so he's sure to tighten and straighten everything.
While in the elevator, Peter starts to relax a little. He loosens his strap like someone would a tie after work then casually strolls around the halls with his pack off and gun holstered.
Ray, however, is anxious and puts his goggles and gloves on, straightens and cinches everything up, gets his pack switched on and leaps into action with his gun drawn.
Also, Ray's belt wasn't just loose or had too much slack. His gloves were tucked into that strap instead of his pistol belt, which caused it to droop. And we see Venkman adjusting something in his belt-area in the elevator. Possibly loosening that strap.