Great game -- I played to the finish and really liked both the art and the creative mechanics. I enjoyed that you left us to figure out how to manipulate the mechanics, as it added an element of logic puzzle in how to overcome various barriers. It took practice, but I liked the challenge. The chaining-together as a plot device reminded me of Hitchcock's "The 39 Steps," where the handcuffed male and female leads jump from rock to rock, he carries her, etc., and they start by bickering but get to know each other over time (quite different dynamic, though!). Nice!
Some feedback I hope is helpful: There are a few points where I think you are missing a collider at the left-hand edge of the visible gameplay area. In the scene shown below, I grabbed the key and continued to the left (the camera does not follow) and fell right out of the game world. I thought it would be a soft-lock but you helpfully have the Reset Room option. This issue happened a second time in the final scene: after making my way from left to right, floating up onto the second level, and going back from right to left, I tried to alley-oop the princess onto a platform and she went clear off the screen to the left and we both fell (out of view of the camera) back to the first level, and then fell again out of the game world.
I had fun playing this -- really good job putting a complete game together with creative ideas in such a short time!