If you are going up a hill, weight counts. But at a constant speed (uphill or not), weight on a wheel counts exactly like weight on the bike, or weight on your body.
If that extra weight on the rim serves to improve our aerodynamic efficiency, then it's worth it.
The Proof
Let's do a comparison: Mr. Lightwheels weighs 165 pounds, and rides a bike weighing 17.6 pounds. His twin brother, Aero, is exactly the same. Both can maintain 250 watts of power output in a 40K bike leg, and both face identical wind drag, except for their wheels.
Mr. Lightwheels has conventional wheels lightweight box-section rims with 32 round spokes. Aero has something like Tri-Spokes. (Pick your choice of aerodynamically optimized wheel; I'm using typical numbers.) Standard wheels aren't much lighter, if at all, than aero wheels, but just for fun let's say the conventional wheels are ultralights weighing 200 grams less per wheel.
More: Do Lightweight Wheels Really Make a Difference?
In a flat 40K time trial, who will win the rider who is lighter, or the rider who is more aero? The answer is the rider with aero wheels will finish more than 28 seconds ahead of his lighter brother.
This includes the effects of the startup acceleration. Even if the bike leg goes steadily up a 3 percent grade, the rider with more aero wheels will win. Only when the grade exceeds 3.7 percent does the bike with lighter wheels have the advantage. And that's 3.7 percent over the whole race, not just the uphill half of a rolling course.
More: 5 Tweaks for Speed
Aerodynamic Wheels vs. Flyweights
Other analyses have shown aerodynamically efficient wheels are always better, even in bike racing events like criteriums, with the exception of hill-climb events. Even when they weigh more, they are better.
In a flat 40K time trial, the aero wheels would have to weigh many pounds more before their weight soaked up their aero advantage.
That takes care of the wheels, but what about weight elsewhere?
More: The Effect of Weight on Speed
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