The pony I ride wears a neoprene (I think that's what the trainer said) girth. It's kind of stretchy all over. I had asked her why a few lessons ago, and she explained that it worked better because the pony is "girthy" and explained what the term meant.
Yesterday I got to see it for myself. I always do the girth loosely at first, and then tighten it a little more in the arena. Yesterday I fastened it loosely as usual and pony started side-walking and h body looked like the saddle was impossibly heavy - almost like she was dipping down and ready to collapse (or kind of staggering like a drunk person, having a hard time describing it). She went forward a little and I started to get scared that she would then start to freak out about the cross ties. So, I told her whoa very gently and quickly loosened the girth even more and she calmed down. But wow, it all happened so quickly and was kind of scary!
I'm glad we had discussed it earlier, or I would have had no idea what the cause was. I'm also really proud of myself for staying calm and thinking quickly. It's so apparent to me that when you're new there is so very much to learn.