Gravity is indeed a relatively weak force, but it has two things going for it when it comes to creating galaxies. Firstly gravity is always attractive and additive, so the total attractive force scales up with the amount of matter. Secondly for a ball of stuff of radius $r$ the factor $M/r^2$ goes up linearly with $r$ i.e. make the ball big enough and it will always collapse.
Would it make more sense to say galaxy is collapsing
The angular momentum of the galaxy is conserved, so the galaxy can't just collapse into a point (or black hole). For this reason I don't think it's appropriate to say a galaxy is collapsing. At some point the angular velocity will increase enough to balance the gravitational attraction and the galaxy will stabilise. In principle galaxies can shed angular momentum by ejecting stars, but this is very slow on timescales like the lifetime of the universe.