Just as some hotel rates require a minimum number of nights stay and some airfares require a Saturday night stay some rental car rates have similar requirements.

Typically, weekend rates extend from a Thursday noon pickup to a Monday noon return so your Friday-Sunday rental shouldn't stray outside standard weekend rates.

Also, when you said that the prices are now twice as high, did you mean that you searched for a new reservation or just changed the pickup time on your original reservation? If you did a search for a new reservation it's likely that the fare "bucket" your original reservation is in is full so any new reservation would be quoted at a higher price, but by modifying your existing reservation with your new time you should stay within your original bucket. If you saw the higher price when you changed the pickup time on your original reservation there's a good chance that there's some requirement of the original rate that's not being met by the new pickup time.