I don't think a 300 lb weight limit solves the problem.
QB concussions are the result of a QB getting blindsided. Concussions happen all the time in high school where the average player weight is nowhere 300 lbs. Concussions are sometimes the result of intentional helmet-to-helmet hits, like a running back lowering his head as he heads into a tackle, but an awful lot of concussions are a result of an unprotected player being aggressively hit by a very fast moving and unblocked defensive player.
And really, that's where a lot of the non-brain injuries stem from as well. Offensive players, particularly QBs and receivers are at certain times almost completely unprotected and yet completey fair game in a way that isn't allowed in boxing, for example.
There are some defensive players, in my opinion, that are savage animals and totally unload on an unprotected player. They do it, because the rules permit it. You can make a great tackle without trying to destroy a person.
It's a judgment call, but particularly for a receiver that is running a route over the middle, or the blindside of a QB, it seems to me that a slightly dialed down tackle would have netted the same result for the defense without injuring a player.