What is thought to be most responsible for the salinity of the oceans
Rivers, evaporation, and rainfall. Salt collects in the rivers in multiple ways. From there the salt flows down the rivers to the ocean. When water evaporates from the ocean it leaves the salt behind causing mass amounts of salt accumulation. However the water that evaporated eventually turns into rain again causing the rivers to flow and bring in more deposits of salt to the ocean. Think of it like the water cycle just with salt!
(late on this... but for everyone else that needs a simpler answer)