Here are the options as I see them:
Trailers accepted at Sunset Marina – coat for vehicle and trailer somewhere around $30 /day. Easy launch. Phone for info. Might be full.
Trailers probably not accepted (as far as I know) at BC Ferries or nearby street level parking and as Quirine says, costs $20/day for a vehicle so maybe both for $40/day? Bit awkward to launch in the bay – there is a private launch but it has no parking. The public beach is next to a public park and means carrying up/down the bank or launching off the public float at the end of a long dock. Parking is killer even while unloading/loading.
Gordon mention the old section of Hwy 99, by-passed by a newer section of road. This is free but hence it is scarce and spaces are only likely if you arrive mid-week at some early hour and I would not expect to be able to also find any space for a trailer.
Lastly there is the Lions Club ‘overflow parking lot” on Marine Drive, also used as a park-and -ride for commuters weekdays. Not suited to a trailer, but you could ask in advance. They are not staffed/ taking payments until Easter. They have usually charged $30 for a vehicle for 3 days Fri/Sat/Sun. Otherwise free. It’s a 10 min walk from the public beach.
I’m unclear why you would choose to bring a trailer – do you have more than a full roof load of 3 kayaks to transport?