Ocean tides are caused by the gravitational effect of sun and moon on the water bodies. Being about 400 times closer to the earth than the sun, the moon has greater influence in creating such tides, although it is much lighter in mass. The greater is the pull, the higher goes the high tides (and lower goes the low tides too). Rotation of earth makes the daily tidal cycles over a particular place.
As the gravitational pull is dependent on the distance between two bodies in space (`F=(GMm)/R^2` ), the height of the high tides is definitely dependent upon the astronomical factors like distance of moon from the earth. If the distance between the moon and the earth were doubled, the gravitational pull of the moon on earth would have been a quarter to what it is today. Height of high tides (and depth of low tides) would also have reduced then, albeit by a lesser degree. This is because, the unchanged gravitational effect of the sun would have 'masked' the effect of a distant moon somewhat.