Natural satellites for Mercury Would it be possible that Mercury had a natural satellite but the gravitational pull from the Sun became so overwhelming from it growing over the years that it just sucked in Mercury's moon?
The larger an object is and the further away it is from the Sun, the greater its Hill Sphere is. Mercury's is very small (only about $175000km$ in radius from what @userLTK said) and its "moon" would therefore be yanked away by the Sun relatively quickly. See this for more details.  The orbit of this moon would be highly unstable and therefore unpredictable, so it may hit the Sun.