First off, your weight does in fact change, you are not imaging it.
Second: The difference is tiny. Easy to calculate, but tiny. Remember, the Moon moves the tides, not the Sun. Not because the Sun does not create an effect, but because it is swamped by the larger gravitational effects of the Moon.
Remember, the gravity effects of one body on another are proportional to the distances. So while the Sun is Really, REALLY big, it is so far away that unless you have a planetary mass, the effect on you is almost non-existant compared to say the mass of the moon which is trivial by comparison but because it is so much closer the effect is vastly (if still tiny) larger.
When in doubt, check your local tide charts. At Neap tide you weigh a tiny amount less, and at Ebb tide you weigh a tiny amount more.