The few times I’ve tried weighted chinups and the weight gets much above 50 pounds, I’ve had problems with elbow pain that seemed to be tendinopothy. I’d usually return to unweighted chinups or lat pulldowns (or both) and the pain would resolve. Progression would be something on the order of once a week do 3 sets of 5, next time add 5 pounds (later reduced to 2.5 pounds) if I could do 3 sets of 5, increase weight, otherwise increase reps, repeat.
Based on my reading of some of your materials, the problem could be a load management issue, specifically, that I was increasing weight / stress too fast and the solution would be to try weighted chins again, but progress very slowly.
Have I provided enough information for you to have a view on this? If so, does this make sense and how would you progress weighted chinups? If not, what other information can I provide?
It’s a bit difficult to pin down a clear mechanism here, because the elbows aren’t “only” seeing the stress from the weighted chins, but rather the cumulative stress being applied in the overall program at any given time. I haven’t done weighted chins in years, but had a similar experience when I was training them regularly as well.
To be fair, your prior attempts at progression sound reasonable, but if you find that things get sensitive every time you try that, it sounds like you need a different approach. There is no “correct” answer here, but rather a variety of options that you may need to experiment with if the weighted pull-up is an important lift to you.
For example, you could do 2-4 “ramping” sets of 5 (or any rep range), rather than sets “across” and see if you tolerate that better. You could do one top set with lighter weight back-offs (or bodyweight backoffs, or lat pulldown backoffs, or tempo lat pulldown backoffs), 1-2 times per week. You could alternatively periodize things a bit differently, starting out with a period of higher-rep, lower-load training (starting with sets as high as 12-15 reps, which is what you see with many of our rehab programs) and ramp the load up and reps down gradually over time, in order to build up the tendon capacity.