While I understand that there is much more to the discussion than weight, 6.3lbs is probably not going to make that much difference and that is one of those things that makes the "how big of a tire can I run" threads difficult. There are a lot of factors and you can save 6.3lbs by your choice of rims. The leverage is a bigger factor and the weight only exacerbates the problem.
You can cheat on your spouse, your taxes, but you can't cheat physics...
Even a lighter 37" tire and rim combo will be much harder on stuff than a 35" set up.
Let's discuss the JK44.
I understand the HP side of it, but the tubes, which most everyone agrees are not that strong are the same between TJ D30/44 and JK44's. JK's have proven that their C's are weak. And why if (according to the JK Gear swap thread) D44 R&P breakage is not a problem are JK44's an upgrade to TJ44's by simply being a HP?
The internets is a funny place. Ask any JK owner and most TJ owners how best to strengthen the JK 44 front and across the board they will tell you to buy the internal sleeve kit and get after it.
They will also tell you to fix the inner C's and then do the same for the TJ front axles.
The issue with all of that is the internal sleeve kits are only good for holding the tubes in place to line them back up after they break in half and the TJ simply doesn't now nor have they ever needed them and they don't work on the axle that does.
Then we have the Inner C braces and the ratio of bent TJ inner C to Wallowed out balljoint holes doesn't support their use. I've seen far more ruined balljoint holes than I ever have bent inner C's. The funny comes into play due to the non warranted trickle effect of fixes for the JK 44 now being recommended for an axle that never needed them and the only part of them that actually does some good, the C braces really aren't needed.
Is there an upgrade to a JK44 that is not available for a TJ44? Up to 35 spline inners? Check for both. 32 spline outers on JK's? Yep, but possible for TJ44's without much effort. Larger "1350" sized u-joint for JK Rubi44 vs. the 1310/760 u-joint of D30/D44? Yep, but again, larger u-joint possible for TJ44. RCV axles: the "bell" of the CV is the same for both axles.
Why is a JK 44 an upgrade over the "weak, not a real d44" axle from a TJ?
Width if needed, Pinion height if you can use it, and maybe the use of the Reid knuckles. After that, make sure it fits what you are doing because it's not exactly an easy swap and the brakes are nothing special.