A heavyweight boxer isn't the same for both sexes. If you mean coupling heavyweight against featherweight of the other gender or something similar to compensate, it could work but would probably be seen as unfair, it would be hard to draw the line on where it's equivalent.
I do think it would be interesting to have mixed team sports where a certain number of each gender needs to be on each side, but it would probably end up with positions always being relegated to the same sex.
The definitions aren't the same, but that can be fixed: heavyweight = over 90kg, whichever gender (right now it's 91kg for men and 79 kg for women). They'd compete against each other in the same weight class by actual weight, not name of class.