Increasing RAM from 4 to 16GB will only help if a) you have an edition of windows/SQL Server that can support that much and b) if 32 bit you configure various things properly for the memory above 4GB to be used.

Having said that, extra memory will still only REALLY help performance if you have either a small database that can sit in the larger memory or you have sufficient IO bandwidth to keep pages flowing into the buffer pool quickly. Almost all implementations I have come across in many years of consulting have a big win from quadrupling their RAM though!! 🙂