Not at all. Yes you're accelerating and decelerating a little on each pedal stroke, but the energy requirements are independent of the weight. A heavy bike (or one with heavier wheels) will actually decelerate a little less than a lighter one due to its greater inertia. So while it takes more energy to accelerate the heavy bike you don't have to accelerate it as much and the energy needs are essentially the same for both. In both cases, the energy needed to keep going at the same average speed on level ground will be determined by air resistance, mechanical inefficiency, and rolling resistance.

The first is by far the most important and is unaffected by weight (in fact some aerodynamic wheels are heavier as a result of the deeper rims), the second is small and also unaffected by weight (although higher quality components may tend to be both lighter and a bit more efficient), and only the rolling resistance goes up slightly with added weight - but is a very small part of the total drag.