I am 6'2" and 112kgs (about 15kgs over my fighting weight).
Just starting to regain strength and fitness and I use a 12 kg bell for Turkish getups and one arm swings and a 25kg bell for two handed swings, I would be fine with a 16kg bell for the TGU's now after a few weeks of the 12kg. I alternate between the 12kg and the 25kg doing swings etc depending how fatigue I am feeling. will buy a 16kg bell next.
For back strength and rehabilitation (recovering from a back injury myself) I can recommend doing Swings, Turkish get ups and Goblet squats (great for the opening the hips). . Also worth doing a few one on one sessions with a good trainer to sort technique, I did and it help heaps with the swing and TGU's.
"Times fun when you are having Flies" Kermit the frog