Michael J
The expansion is not actual velocity in regards to time dilation. The space between gravity bound systems is growing larger, the gravity bound systems(galaxies, groups and clusters) have an intrinsic velocity(their velocity through their own local space) and an extrinsic or apparent velocity(the velocity that they APPEAR to be moving away from us) that is mostly due to the expansion of the space between us and them. While it may appear that they are moving away from us at near light speed(and, in fact they are), they are not actually moving at relativistic velocity in relation to their own space so no dilation effects occur(or, at least very small effects due solely to their movement relative to their own frame, not ours).
We seem to live in a privileged time, in that the farthest galaxies are not yet traveling above lightspeed in relation to us. This may not BE true, but some interpret our observations that way. The Universe seems to be about 48 billion light years across. This includes the 13.7 billion lys that light has traveled since the BB+the amount which the Universe has expanded in those 13.7 billion years(including the initial inflation period)X2, if I am not mistaken. Of course, the geometry of the Universe appears to us to be inside out(IE, no matter which direction we look we are looking at the "center"(the BB) where it all started).
Another thing to consider is that when we look into deep time we are seeing those galaxies as they were 13.7 billion years ago, not as they are today. The light that is leaving them today may well never reach us as in another 24 billion years they will have apparent velocities greater than light speed. Also, when they observe our galaxy, they see it when it was a violent, young quasar, not as the relatively calm spiral galaxy we know and love today.
Even in our own neighborhood this is true. Eta Carina is a huge star in the last stage of it's short life. We keep watching it, expecting it to blow up at any time. But, in all likelyhood, it has already done so, but being so far away, the light of that event has not yet reached us.
Hope I haven't just confused you further.
Grumpy