We do weighted chin-ups here. Not exclusively, not as a cure-all, but we utilize them. They have their ups and downs (get it?) but they can prove to be more difficult to progress than other lifts. Whether you're training with us, using a free plan out there like Harry Selkow's plan, weighted chin-ups may leave you stuck at a certain plateau (whether in weight or reps) for a long, frustrating time.
So here's something to try.
I recommend anchoring the weight to your waist with a dip belt OR holding a dumbbell/kettlebell with your feet. For this article, we'll focus on the dip belt. You'll need the belt and some chains (read, the powerlifting type, not the hardware store type).
-SIDE NOTE- anchoring the weight to your waist or lower body gives the added benefit of pulling traction on the spine, decompressing it, which myself and others have found helpful. But that's for another discussion.
As you being doing weighted chin-ups, anchor the chain(s) to your belt at the first link. You are starting out the movement light, and increasing weight as you move through the range of motion. When you have built a certain level of comfort at that load, you can now clip into the 2nd or 3rd link(s). Then work at that level, till you are able to do it consistently for more volume, and then progress to the 5th or 6th link(s). As you progress, you will be pulling more and more weight from the start of the movement. Eventually, you will be able to clip into the middle link, which depending on the chain length, should mean you are pulling the entire weight of the chain through the whole range of motion.
So there you go, a different approach to getting a stronger upper back. Give it a try!