I should stay away from this thread. Even though I have 3 boys I raised shooting and hunting. Currently they are 8, 12, and 22. I disagree with people who say there is only 1 way.
There are so many different variables that play into the "what caliber should I get" question. Going by shooter weight alone is over simplified. There are a lot more variables then that. Brakes, suppressor, stock LOP, recoil pad, grip to trigger distance, comb angle, etc. For some shooters its the concussion for others its the recoil that causes flinch.
Kids are extremely individualistic. My kids are all different in what they can handle. I always let them choose with my approval, of course. Both kids prefer the slightly heavier 6mmCM, 6.5cm over the Howa 6.5grendel I build for them. They say its harder to shoot. I don't really care as its just grab what you are comfortable with. So this year my 12yo and 8yo both hunted with a 6CM. My 12yo made a good shot on a decent muley, slightly quartering away. Bullet struck about the 5th rib forward and midline. Impact velocity was just under 2300fps with a eldx 103gr. Deer staggered and went down. Ended up running off when we got close. There was decent blood, bright red frothy, where he bedded. Horrible experience that we never recovered him. Searched for hours well into the night with flashlights and back the next day.
The next opportunity he used my 7prc, which is overkill I know, but he has shot it enough to be comfortable with it. Its about 13lbs total. He made a 545yd shot taking the top of the heart off and lungs out.
I guess the point is take your kid out and see how they do. It's not wrong to start small and work up. Watch them and let them tell you what they can handle.