West Bay's launch facilities have improved since the new outer harbour slipway was opened. It now caters for much larger boats, and 2012 launching charges reflect this. Irrespective of size, a day launch now costs £18!
without parking, so it does put off some small craft users. See attached photo showing the old slipway (bottom left) and new slipway (centre right).
If this is a bit pricey, the only other option I can think of is Charmouth. There is a campsite 200 yards away, you can park right next to the launch area (not slipway) and fees are very reasonable for inflatables.
It's only a gentle 10 minute jaunt over to Lyme from Charmouth, and like West Bay, there are now visitor's pontoons available. For info, launch fees at Lyme are also £18 now!