Just a few thoughs from my own personal speculation, I,am no aerodynamics egghead (Never met one that was not entertaining though because they can,t even agree with each other) nor am I an Ace pilot but I have to jump in on this one.

Justin, I believe its a bit of a reach when you say "weight has absolutely no effect on absolute speed". Suppose an airplane is two ounces overweight something has to hold that two ounces up, gravity never sleeps except maybe in the movies. If nothing else changes Like increased thrust that airplane is going to descend from a level flight condition with
those two extra ounces if the trim is exactly the same as it was at the lighter weight unless something else is done. The only thing left to do is increase angle of attack to maintain that level flight just enough to support those extra ounces. OK we have just increased lift by increasing A of A and with lift comes induced drag and with drag comes a speed reduction.

Yes and I do agree this differance is a tiny percentage and I seriously doubt anybody could tell much of a differance in flight.

All of the above is just my speculation and refuse to 'incriminate' myself any further

John