According to Weymouth borough council there is no overnight camping aloud in any of their carparks between midnight and 8am. Having said that I suspect its not enforcable due to staffing. I would therefore suggest trying Lodmoor Country park car park, 24 hour toilets and a cafe (which I think opens at stupid o'clock but don't count on that!)
Lodmoor. Its just a 5 minute drive along the front to the ferry terminal then.
Hardys monument gets locked at night, you can camp but you are locked in untill the catering van guys turn up in the morning. Don't know what time that is but it won't be in time for a 6:30 ferry!
West Lulworth is quite a trek if you want to be in Weynouth by 6:30!