Well, if you put the backup back where it was, iTunes should pick up on it again.
Do be sure to disable automatic device syncing (again, check that Devices tab in iTunes preferences) first. With it enabled (as it is by default), iTunes will delete your last automatic backup as soon as you reconnect your device (entirely negating the point of making backups in the first place - don't ask me why, it's Apple's logic).
Backups you trigger manually should not be subject to this issue, and should stick around until you manually remove them. You'll probably want to make a manual backup of your phone's current state before you overwrite it with an older backed up state.
Or, as mentioned, you could use a third-party "not made by Apple") program to allow you to read the text messages in the backup through your computer. Read around before installing software you don't trust, but to get started, do some web searches for "iphone backup extractor" or somesuch.