How does the Moon control Earth's tides?

Instead of thinking of "the Moon going around the Earth," think of the whole thing as a "binary planet system." The Moon is trying to pull the Earth toward the Moon, just as the Earth is trying to pull the Moon toward the Earth. The solid surface doesn't get pulled out of shape that easily, but the liquid part gets pulled toward the Moon a bit.

Its all about gravitational pull. The moon has a gravitational pull that affects matter. Water subsequently is the one of the matters here on earth that is pulled by it. Do you know that earth usually have 2 low tides and 2 high tides?! This is due to also the Suns gravitational pull. However far those two heavenly bodies are they can still affect our gravity. and NO, you don't get lighter in weight when its high tide, if you were going to ask that.