my deck is 10ft off the ground, it is 16x18 and supported by 5 4x4's on double 2x10's (Two of them First one is 8ft from the house, 2nd is 13ft out) it is starting to sway side to side. Will 6x6's stop it or should I look for some other kind of support? The contractor that built it 20 yr's ago said the 4x4's would be suffice

The 4X4's are probably fine,you need to tie the posts together with cross ties.

From the highest point you can attach a 2X4 brace to the lowest point(not on the ground) of a different post,do this throughout the entire deck, make it appear like it was designed that way and you will find the sway goes away!

Hope this helped?

KBC