Velocities of galaxies as they move away from each other I am currently reading A Universe from Nothing, by Lawrence M. Krauss, and I have come across a concept that I found confusing:

Now, if gravity is an attractive force, then it should be slowing the expansion of the universe. This means the galaxy we see moving away from us at $500$ kilometers/second today would have been moving faster earlier.

If gravity was slowing down the expansion of the universe, then should it not have been slower during earlier periods and increased as the objects moved further apart and, therefore, gravitational forces weakened? 
 A: UserLTK's answer is correct but Id like to expand on it. It is not simply expanding out and decelerating or accelerating. The speed at which galaxies are flying away from each other increases as their distance increases, and that is an important and not obvious factor. 
We know this because as the galaxies get further away from us their cosmological redshift increases, meaning they are going faster. 
This has to do with the fact that the spacetime is really what is expanding. What the Big Bang did was to make spacetime grow, and it grows at an average rate, now, of 70 Kms per second, for distances of 1 megaparsec (about 3 million light years), and faster at larger distances so for galaxies about 100 megaparsecs away they are receding from us on the average at 7000 Kms/sec. 
One way to visualize it is to consider the surface of a balloon as you inflate it, and mark 3 points on it, two a distance of 1 inch away, and the third one 100 inches away measuring along the spherical surface. That surface is like our 3 dimensional universe, which is expanding. The point  100 inches away goes away faster from the other two, than those two go away from each other. Our universe is like that surface (except the universe at any one instant is like a flat sheet and you are stretching it, the same idea). The points you drew were like 3 galaxies.
And the universe has been expanding since the Big Bang. 
So, that expansion has been happening, and the expansion parameter is the 70 km/sec per megaparsec. That is the Hubble parameter, now. In the past it was different. The question is how has it changed, and will it change in the future. The Hubble parameter was indeed higher at earlier times, but over the past 6 billion years or so it's been getting larger. Ie, for the last 6 billion years the dark energy, which contributes to the universe mass energy has been dominating more and more (still a small effect, it changes slowly), and we are now accelerating. We decelerated for the first few billion years. The dark energy causes acceleration because it has a negative pressure that counteracts its mass density, and causes a accelerated expansion instead of a slowdown. 
Still ,even now there are galaxies that are going away from us at the speed of light and faster. Those that are about 10 billion light years away (and unfortunately I forget the distance at which this happens, but it is within the observable universe of about 13.8 billion light years) are NOW receding from us faster than light. We see their light because it was emitted before, about 10 billion years ago, and they were not going that fast then.
So, even apart from the acceleration, it is still 'strange' thatgalaxies are moving away faster the further they are. That is because of the expansion of the universe, those further away go faster.   
A: If I'm following your question, you're misunderstanding acceleration or, more accurately, deceleration and velocity.
Before the discovery of dark energy the observation was that the universe was flying apart in a uniform manor, where the further away galaxies were the faster they were moving away, which implies, if you run the clock backwards, everything started out in the same place - hence the big bang model.
Big bang model + gravity implies an initial velocity and a slowing down.  The model breaks down at the singularity, ofcourse, it's not without it's flaws, but the general model works, where, starts out at a point, and bang and everything flies apart very fast.   Gravity slows it down over time and the slowing down (deceleration) is greatest when the galaxies are closer but the slowing down is also cumulative, so while the deceleration is larger when the galaxies are closer, the velocity is larger too and continues to slow over time, meaning faster velocity when the universe was young, slower velocity as it expands.    Think of shooting a bullet so fast it flies away form the earth, faster than escape velocity, the velocity is greatest straight out of the gun, the same place where the deceleration is greatest.
Now the dark energy discovery changed all that.   Velocity or apparent velocity due to the expansion of space makes objects move faster and faster away from us over time, as the distance increases.    It sounds like he's explaining the model prior to the discovery of dark energy.  
(Hope that's clear), the wording is a bit tricky.
