He looks adorable, and I dont think its unreasonable at all to ask a 4yo to canter with a 120 lb rider. I also dont think he’s telling you he can’t, I think he’s just a little lazy when the going gets tough (and the going is not getting all that tough, but that is still a better brain than reactive when the going gets tough).
I just think when he gets a little disorganized, you sit down more and over ride with your hand. You’re just trying to fix it, but my advice would be hands forward, put a little loop in the rein, and three or four strides of gallop down the long side. Even just aiming for that will improve things.
I also think he not definite enough in the up canter transition, and he’s probably ready for a leeeeetle bit more expectation there. You dont need to be a jerk about it, but try to cut down on the “faster trot instead of canter” steps, and also try to have a definite CANTER the first step instead of kind of sliding up into the gait. He’s not terribly disorganized in that trot, but he’s medium disorganized, and it means you have a lower quality canter to work with.
When my horse was a 4yo w two months under saddle we too got the lecture that we can expect more of a big boy canter depart even though we are 4. So if you get more than three steps of the faster trot, walk again (try to walk within one or two strides, so he doesnt learn that he can just drag you around by the bridle), give yourself one or two walk steps to reorganize (no more, or it becomes a break/reward) and then ask for canter again. You dont have to be a rough jerk about it, just methodical, consistent, and clear. This exercise - removing the extra “faster trot” steps and walking three strides before asking again, wash rinse repeat- will improve the quality of the transition as well as his promptness and ridability to the aids.
Then, when you get a step of canter, immediately hands forward, cluck, add leg and ask for three BIG steps. This will help the canter you get in the up transition be definite and with purpose, rather than that barely-cantering-I’m-about-to-break situation you’re currently getting.
He doesnt look weak, unbalanced, or unready, I think you’re just being super forgiving and trying to help him a little too much instead of expecting him to get a little prompter and more definite. Again, you dont have to be a jerk about raising your expectation, but I think if you methodically and fairly set the bar just a little bit higher, he’ll rise to meet it without much issue.
Here is a video of me working on pretty much the exact same thing with the horse in my profile pic when he was 4 and about two months under saddle. The dressage trainer teaching the lesson is great - she really helped us, and I’ve followed and implemented her advice to this day.
Pay particular attention to what she says at 4:38. Following THAT advice has raised my expectation that little bit, and improved the canter transitions much earlier on several horses that came after. 
https://youtu.be/6LLaAcHesDg