Question: Sorry if this question is dumb, but I don't seem to have a grasp on it.

Suppose you are on a rock in space, with no external forces acting. The rock attracts you with a force given by

$$F=G\frac{m\_1m\_2}{r^2},$$

and you also attract the rock with an equal and opposite force. The ground exerts the normal force which keeps you stationary, but what stops the rock from accelerating, however small that be?

Answer: 
Just like the ground exerts force on you stopping you from accelerating, your legs push the rock stopping it from accelerating.
One way to look at is:

1. Newton’s laws (namely action and reaction) implies that both bodies feel the same force (in opposite directions).
2. Both bodies are therefore accelerated, but in proportion to their respective masses $a = f/m $., therefore the most massive will appear not to move noticeably (compared to the other one), but it will move nonetheless, albeit in a relatively small way (determined by the ratio of the respective masses).