The slipways at the Sailing Academy are open for use but you need to check in as a day member (£20 for up to 6M I think + £3 ish harbour fee). Info on their website www.wpnsa.org.uk
Can launch at all states of the tide.
May seem expensive but great facilities, seperate slipways for the dingy sailors and RIBS, yacthies also use the slip with the crane lift. Also has a great cafe and freshwater taps all over the place to flush/wash. Some great cruising/wave jumping along the coast to Lulworth (nice ice cream shop) but don't go any further if the ranges are firing! - or into Weymouth Harbour for an 'orange juice' in the pub.
Bluwater Horizons by Ferrybridge launch your boat for you with a tractor, bit cheaper but not so many facilties and a bit of a race through the channel.