I agree with what most have posted here-he does not look 'uppity' to me. He has a nice rhythm at the canter and does not appear to be rooting or jerking.
What I do see is some stiffness behind, i think from the stifle. He takes an occasional step outward (like a half circle rather than straight line following his front feet) like he is avoiding something higher up than the hock.
Also, at the canter, I would try a half seat, and loosing your arms from the shoulder. Your hands should be following the horse's natural motion with his neck that goes up and down, or in your arms' case, towards his ears and back towards your body. Your arms are quite stiff, which is popping him in the mouth every time he takes a stride forward and his natural head motion goes down/out.
I think there are a few things going on. the lack of fitness, time off, possible hind end stiffness and a stiff rider. I know that it is hard to 'let go' with your hands and trust the horse to stay in his rhythm, but you have to make your hands and arms more supple through the bit. With practice, you will get it. I would start with a half seat and placing your hands right on his neck at the martingale-you will feel his natural neck motion at the canter, and eventually you will be able to sit back in the saddle and let your arms 'follow' that motion.
I watched your video a few times, I didn't think he was too strong at all as others mentioned. I have a few suggestions that might help you out. The first thing I would do is purchase a gel pad to put between your saddle and the fleece pad. The gel pad will help absorb the impact on his back while he develops more muscles.
The second thing I would do if I were your coach, would be to ask you to sit up and put your shoulders back at the posting trot and the canter.
He won't be able to pull you forward as easily if you are centered and you can use your back to brace in the half halts.
While you are posting ask him to stretch his neck and lengthened his frame by vibrating the inside rein and yielding to him. Let him take the reins out of your hands and stretch down while you maintain a forward trot with your shoulders back. Gently shorten the reins and bring his head back up asking him to remain round by vibrating or flexing your inside rein.Practice lengthening him and shortening him at the walk and posting trot, it will help him to develop his muscles. He looks like he's a lot of fun!
Thank you all so much for your feedback, I read all of it and need to clarify -
He does toe out in the left hoof, just how he was born :P And he has been getting hock injections for about 2 years since he has arthritis in the back left hock, but has always been a little stiff in the back end for as long as I've had him.
I definitely have to work on my fitness too, and I know I stiffen up when it feels like he's going a little too fast for me, so I'll definitely work on that - as far as getting a friend to help, I actually have a saddle buck from an old tack shop and I can get my bf to be a darling and help me with that! Sitting up and back with nice shoulders has ALWAYS been a problem for me, and I am definitely going to re-read all of your advice again and again!
I see you bracing yourself as if you are anticipating him getting quick down the long side, so hes inverting himself to get away from that and thats where you're feeling him get strong. Soften your arms and let them move with him. If he gets strong, give him a little check but pulling on your reins upward very quick and then soften immediately. Remind him he cant invert himself like that. I also see you leaning to the inside esp at the canter, which is probably throwing you both off balance. Try to focus also on stepping out and putting more weight into your outside heel to balance better.
He is very cute. You look great on him, just remind yourself to breathe and relax your arms.
You guys look good and your horse seems to have a good canter rhythm, but I see what the poster above sees, which is a tilt to the inside. It looks like he falls in at the corners and you lean with him (or maybe you start to lean first and he goes with you). Either way, it looks like when he leans in he drops his head and you are left carrying him through each turn. When you canter into the corners, try putting your inside knee against his shoulder to keep him from falling in on it, and support his body with your inside leg and steady outside rein contact as he goes around.