I'm a big guy, 250 lbs +, a former power lifter and a nidan but I have fragile elbows. Lots of times I've asked much smaller men, women and kids to take it easy on a technique because they were tweaking my elbow. The is no shame in protecting yourself!!! Beyond not hurting your partner, your other primary responsibility is to not let yourself get hurt. So tell the guy to loosen up!
Also, as someone who I am sure did that to peoples arms when I started, I bet he just thinks he's giving a committed attack. He probably doesn't understand that when he holds that strongly he is giveing up relaxation and can't really feel what is happen in either his or your body. Ask him to try using an open palm and try to feel how you are moving. Do that with him too. It may cause something to click for him.