Both of the sites Bigal mentions have the benefit of being on the West side of Weymouth giving direct access to the sailing centre without the need to go through Weymouth. Spectacular views over Lyme Bay to the west too. At the site Alan recommends – Pebbles – the tent pitches with hookups are in the most sheltered spots while the top field is really spectacular in terms of sea views but you might need to make sure you can reef the tent! Alternatively there are fixed caravans for hire.
There are sites to the north and east of Weymouth but travelling through Weymouth every day would be OK if you like to worm your way through the traffic – you’ll have plenty of time to view the holidaymakers on the beach!