I just flew the 172 just now. It’s pretty twitchy in live weather, but, as @CharlieFox00 has said, a slight touch of a joystick can impart a ton of force in the sim, so I blame that more on my joystick and the fact I was getting knocked around a bit by the atmosphere than anything.
It was definitely necessary to keep it at about 76 knots or a little better to maintain a 1000 fpm climb (I forgot to check W&B, 
but assume I was at half fuel with just a pilot). It was also easy to pitch the plane to 2500 fpm, but I definitely didn’t leave it there for long.
So… As I noted above, for those having this issue, make sure your trim is set for takeoff (you can see the little white bar to the left of the elevator trim wheel), let the plane lift off between 55 and 70 knots (I usually let it get to 60 to 65 knots before I lift off), let the plane accelerate to 76 knots then pitch and trim to that pitch for about 1000 fpm climb (assuming your within a 1000 or so feet of sea level) and then make sure to trim for level flight when you reach your altitude and reduce throttle to 2200 - 2400 for cruise.
Plane flew nicely and I greased the landing 