Weight IS important, but relative to a person's frame. In other words, we should not sacrifice strength for a lighter body.
It's power to weight ratio that is important, as it is in Chin-Ups.
There are people who can't do a single Chin-Up who can Lat Pulldown many times what someone who can perform 30 or more Chins can.
When I was under 5% body fat, I could run sub 15 mins for 5K, but now struggle to go under 19 mins at 16-18% body fat.