We both post on GP3S and I know that we are the same weight, so this might help.
The flat vee bottom shape means most brands will work well on the iS137. I've only had my iS137 carbon for 2 or 3 months and Im still going through the tuning stage. But this what I have found out so far
I found that the old iS144 and 9m warp worked very well with a Select RS7 51cm. The 51cm was a perfect "do it all" fin for heavy guy's, this gave a massive range from 10k to over 20k in any water conditions. The iS137 carbon is a bit more fin sensitive. I think this is because carbon feeling is very different from wood.
Unlike the old iS131/144, I do not think you will get away with just one fin. Two or more fins are needed. The RS7 51cm is working great in 8k to 15k. After this, the RS7 51cm is to much and not needed. The sharper rear rails help to displace water better than the older iSonics so smaller fins are needed.
I have bought two additional fins for testing, a Select S10 47cm and a Vector Canefire 48cm. I am still working out which fin works best/fastest in above 15k winds. So far, I like the feel of the S10 47cm, but I think the new S11 49cm might have been a better choice for "all round" speed (this is very similar design to RS7).
The Vector is also nice, but different feel than the Select. Its a bit softer (G10) than the Select and is a lot heavier. The Vector does cost a bit more cash as well. Both are good, but I use Select for years and got used to their feel.
I think that the best solution would be 3 fins, 46/47cm (strong wind), 48/49cm (medium wind) and a 50/51cm (light wind). But this will cost plenty
For two fin option, one slightly above and one slightly below its sweet spot 49cm and 51cm should cover it.
For one fin option its got to be 50/51cm for a heavy weight as you will struggle more on a 48cm in lighter winds.