Full Moons get the highest tides not because of the Moon but because of the Sun. The Sun’s tides on Earth are about one-third the strength of the Moon’s tides, yet hardly anybody talks about them. During full Moon, high Sun tides add directly to high Moon tides, giving the false impression that the full Moon imparts extra gravitational influence. Furthermore, whatever false gravitational influence you ascribe to the full Moon, you must also grant to the new Moon because the Sun’s tides perfectly align there too.