What's the problem with micro accelerations when climbing? With every pedal stroke your bike accelerates a bit. But between the pedal strokes it will decelerate..... With a heavier bike the speed will be more constant, that's all.... of course a lighter bike will climb better, but when riding uphill with constant speed it won't matter wheter you have a 1300 gram frame and 300 gram rims or an 1100 gram frame and 400 gram rims.
By the way, I have seen studies which show that even on a relatively steep climb a heavier, aerodynamic wheelset is faster than a light, non-aero set. (But LightWeigths are both light AND aero