What is also odd is GC pros will drop down to crazy low body weight at the expense of power and then ride bikes that are heavier than they have to be.
It seems that way but I guess there is more to it or there is something I have not accounted for.
Not all do. The top contenders used to run special setups not so long ago (Lance with his front shifter). I'm sure they still use special wheels for the mountains. And thats where the weight can be gained (especially considering the sponsor deal limiting choices).
What I find the most amusing is that pro's don't use the lightweight saddles. Practicality first for sure!
Related: The mass effect on acceleration: It's tiny in cycling, even in the rims. Consider that normally a sprinter accelerates 5 km at max and this at a relatively small wattage.
Weight is only an issue when climbing. Even wheels (if not ridiculously heavy) don't matter that much, simply because there is hardly any significant acceleration/deceleration.