Hi Ronald - I think the OEM cables were smaller than 3/16" but when folks replace them, they tend to go with 3/16" because they have higher tensile strength and they will fit. As I told another member, you don't really need a HUGE amount of strength, because the load of the top is distributed across four cables. So, if your top weighs 1000# (and most are less than that unless you have a really big trailer), each cable has to hold 250#.
1/8" galvanized wire rope at Home Depot has a working load limit of 340#. Their 3/16" galvanized cable has a working load limit of 850#. A better choice, in my opinion, is 3/16 stainless, with a working load limit of 740#. Cable breakage occurs when the cable rusts and then it is bent sharply over the upper pulley. Stainless solves the rusting problem if the cable is not lubricated properly.
- Jack