If we're talking about steady-paced riding on flat ground, basically wrong. There are technically some subtle physics differences, but nothing that's measurably impactful.

Gravity pulls harder on heavy objects than light objects.

When you go downward through Earth's gravity, you receive power from that gravity. If your bike+rider system is heavier and gravity is pulling harder on it, then you get more power. So you go faster, just like you would if you added power by pedaling harder. (Assuming that whatever you did to add weight didn't increase other drag forces).

The benefits of extra weight on the descent generally don't make up for the penalty of that weight on the climb, though.

It could, if those heavier tires did not increase the rolling resistance.

All other things being equal, a wheel that's heavier at the rim will be accelerated slower by gravity downhill (due to the mass being rotating), but have higher terminal velocity (just like all added mass).

How those kinds of positions feel varies a lot by the particular handlebar arrangement. Especially when you get into the phantom-aerobar-esque realm of gripping the hoods from the inside.