The controls are a bit finicky. Player movement is slow and also sometimes I wasn't able to jump when on the floor. I kept sticking to walls. You should add a physicmat2d without friction to the player just so it doesn't happen.
You don't really have any incentive to stay on the slim platforms. Maybe make it so the player doesn't want to stay on the wider platforms? I mean, if it's a rain then maybe every once in a while there could be a lightning bolt hitting those platforms to keep you on your feet.