Yeah why not run some spectra or dacron backing on those work horses? Maximize you spool capacity and line strength, depending on what kind of fish you're getting into. Mono is pretty standard when fishing Tiagra 130's and 80's, but there's no reason why you can't put some 130lb backing with an 80 or 100lb topshot on that Tiagra 80. As for the Tiagra 130, step it up to 200lb backing with any top shot you want <200lbs.
Up here in New England it's pretty standard to run 200# dacron on your 130s with a top shot of 130 mono. As for the 80s it all depends on what you're going after but 80-100# dacron or 130-200# braid is a pretty safe bet.