Bouldering places a lot of strain on the ligaments and tendons of the arms and fingers, moreso than weight training alone. It becomes particularly evident when you realise that you're having to hold yourself in a static position on the wall, keeping your arms locked at particular angles instead of steadily working through the full range of motion.
Yes, you are quite heavy for a climber. At my heaviest, I think I was just under 110kg and climbing / bouldering several times a week. That means that you're going to be placing a lot of stress on your joints (particularly fingers, elbows and shoulders) and since tendons take longer to strengthen than muscles, things like pulley injuries and elbow / shoulder complaints are fairly common.
Chances are, the pain you're feeling is because of unfamiliarity of the complex movements involved in bouldering, and as you yourself allude to, technique issues probably meaning you're relying on your upper body strength a fair amount, particularly on overhangs.
The answer for this is basically time and practice. Assuming you're taking care of recovery and nutrition, your body should adapt to the demands you're placing on it.
If you want more specific recommendations, then I'd try and climb on different days to when you lift, or at least leave a decent amount of time between the two (i.e. climb in the morning before work, lift after, or vice versa).
Also, use your feet more. Don't try and power up overhangs, deliberately place your feet, turn your hips into the wall, use heel hooks to take the pressure off your arms and hold yourself in the wall, don't grip the holds as tightly, watch female climbers and see how they tackle problems that you find yourself powering up, move slowly and with control instead of dynoing from hold to hold.
Stretch your forearms before and after bouldering sessions, and get yourself some soft tissue work on your forearms. I've seen tight muscles and muscle knots in the forearms cause elbow issues for climbers before.
I've made a fair amount of assumptions there, but they're all based on several years of introducing new people, male and female, into climbing and bouldering and observing the most common mistakes people make.