To not answer your question, far less than water weight changes affect it... =)

Well, in round numbers the moon is 4E8 meters away and has a mass of 7.35E22 kg. G = (6.67E-11 N*m^2/kg^2) so it accelerates you at 6.67E-11 * 7.45E22 / (4E8)^2 = 3.106E-5 N/kg. Your weight due to Earth's gravity (little g) is 9.8 N/kg. So, the moon varies your weight by about plus or minus 0.00032%.

These are rough numbers (particularly, the moon's distance from earth varies quite a bit between apogee and perigee), but that should be correct to well within an order of magnitude.