I had a listen to your recording.
Pros:
- Your pitch is good, even on high notes. A few notes out of tune but not many (listen to 0:40, slight pitch problem there)
- You're not putting too much weight on the high notes
- Rhythm and timing spot on!
Cons
- No power! Your voice sounds even softer than normal talking.
- No vibrato, which probably indicates some tension in your voice.
- Voice unstable at 0:47 (sounds about to break)
I think it's the lack of power that is the weakest point. But you have to be careful not to introduce tension as you increase power. It's hard for me to make suggestions, as my voice is the opposite of yours - I use too much weight, but you use too little. The advantage of light singing is you already have a huge range, but you really need the power now.
Are there any notes inside your range where you can't sing because your voice is too unstable?