My weights setup is in the garage attached to the house and my little boy's bedroom is the other side. So no weights after 6pm for the last few years which is a pain, especially if I don't get home by 4:30pm.'
So I cut some carpet underlay to go over all the supports on the rack, built it up to 1 1/2 inches (3 layers) and wrapped it all in duct tape. Worked really well!
The hubs is a glazier so we have these little pads everywhere. They are about .5 x .5 and they are rather thin. Anyone's local glass place probably has a bunch of them out back with the pallets the glass comes to them in, you can probably pick them out for free. We have them everywhere from doors that will slam if one isn't careful to the rack where the bar rests. (Because if I'm too loud the pig comes over to "help".) They are handy little fuckers.
You can also do some soundproofing on the common walls. Can go all out in this regard, but even one layer of green glue + one layer of drywall over your existing wall is pretty easy and cheap and makes a big difference.