Are your running backstays
truly "running", as in, removable? If so, I assume you have a length of line with block and tackle on the end of each? My running backs are vinyl-coated stainless with 4:1 tackle on each end made of 7/16" double-braid polyester (Sta-set). When I replace the vinyl-coated stainless (will be soon), I'll use 5 or 7mm Dynex-dux, which is $1.79 or $2.99/ft respectively. It is very strong, durable, easy on sails
, can be (very) easily spliced, and light.
Dynex Dux - Colligo Marine
You can read more about Dynex Dux here
If you don't want to go that route
, use 7/16" or 1/2" double braid - but it'll degrade faster, stretch a lot more, whip around and make noise
, and have a lower breaking strength (especially after a year or two of sitting).