Very fun retro style game! Great music and game feeling. I made it through the first 10 levels and played the first with the throwing items.
When the player responds sometimes, they appear to hover in the air for a moment before landing on the platform. I noticed the same when the player responded at a checkpoint. Are all of your spawn points with the flag, and the player is "hovering over" a invinsible flag? If so, that's clever on reusing your resources!
I really appreciated the forgiveness you give the player with constant checkpoints. It makes the game fun when retrying difficult portions without having to waste time getting back to the point from the very beginning. My only critique with it though is that I noticed that the checkpoints default to the last touched, so when I accidently jumped off the cliff on top of a older checkpoint, it defaulted to that one to respawn me despite me reaching the further checkpoint. Maybe that was intentional, if so that's totally fine; for me it's a player preference that I would default to the checkpoint closest to the end that the player has reached.