Your "probably" means you've refused to look at the relevant experimental evidence?

"proportional to mv²" also means "proportional to 1/2 mv²" and "proportional to 123.45 mv²".

Assuming your gravitational and inertial masses are supposed to be the same, then 1/2 m v² is, by Noether's theorem, a consequence of conservation of energy. https://en.wikipedia.org/wiki/Noether%27s_theorem#Example_1:... .