it does. I assume you are talking about tides, as waves are caused by wind, not the sun. Tides are caused by the attraction of the sun and the moon. There are tides on dry land as well, except the effect is too small to be felt. It's only because the oceans are so large and fluid that it can be seen.
"shouldn’t we fall forward a little bit" ? no, first of all, the pull is upwards, and second, it is too small to be noticed.