Very cool use of the limitation, factoring weight into platforming. Short, but not a bad puzzle. Great first effort. Also, the visuals are great.
A couple of suggestions:
-The main character should move a bit faster. When the movement is too slow, it feels frustrating for the player.
-Add some music and sound effects. A little bit of effort goes a long way in the audio department--even mediocre sound effects (as long as they're not too grating) make the game world feel much more alive. You can look into the utility bfxr to create old-school sound effects, and look in the Unity Asset Store for free music you can use in your projects.