I'm 130 lbs, and my gelding is about 14 hands and built like a TANK. He could easily carry three times my weight. And he will still try to jig around when I get into the saddle, western or english. So does my 15 hand gelding, so does my mom's (EXTREMELY undisciplined and rude) mare. All of them are good, strong, stocky horses who could easily pack 300 lbs. I've only ever seen one horse that looks weak enough to not be able to carry more than 150 lbs, and that was just being safe because of a VERY weak body type.
I know my horses are healthy, etc. They do that because I spoil them, and it doesn't really bother me because when I want them to quit, they listen.
What do you do when you get on? I think this is just him misbehaving for you.
I would analyze what YOU do, then what your trainer, who he stands for, does. See if there's a difference, because I think that's it. He's being spunky with you.