As far as I know, Royal Mail won't accept pre-paid USPS-labeled envelopes. However, you can ship from the US to the UK using the USPS flat-rate international express envelope for $45 if you buy the label online (you'll still need to get the flat-rate envelope from a post office).
For the return shipping, these would be the steps:
1. Weigh your complete application packet. UKBA will send back most of your documents and won't add anything extra, so you can figure out the weight in advance without worries.
2. Buy a pre-paid label from UPS or FedEx. MyUPS on the UPS website tells me that Express Saver shipping from the UK to the US would be $41 for a 1.5 kg package (just using that figure as a random estimate). I don't have an account with FedEx, but I'd guess it'd be similar. You can do it all online with UPS (and, I assume, with FedEx) but, if you go that route, you'd still have to pick up the appropriate UPS or FedEx envelope from a physical location.
3. Attach the pre-paid UK-to-US label to the appropriate empty envelope, add it to the pile, then chuck it all in the envelope you'll be using to send US to UK. Send the lot using the service of your choice.
Not sure what the difference is between online and in-store prices for UPS and FedEx, but I do know that the USPS offers a discount for online label purchases. It might be more convenient to do it all in one fell swoop at a UPS or FedEx location.