Louis Harris, 18, has been missing since he was spotted near the pavilion walking up steps towards the pier at 04:30 GMT on 14 February.
Dorset Police said it was "totally out of character" for him to disappear and they were "extremely" concerned.
A spokeswoman added that specialist dive teams have been looking in Weymouth harbour.
Mr Harris is white, about 5ft 10ins, slim, with brown short hair.
He was last seen wearing a blue and white hooded Lacoste top, a white Fat Face checked shirt with a blue and red checked pattern, blue jeans and Vans shoes.
Chief Inspector Steve Horton, of Dorset Police, said his family has not heard from him since he went missing.
Police divers have been searching for a missing Dorchester man who was last seen on Weymouth beach.