I'm fat (170 cm 102 kg). I go bouldering about 3 times a week.

It's a lot harder when overweight. I haven't progressed as fast as everyone around me, and it is frustrating watching people who aren't overweight climb for the first time because they typically can do things I can't. It's also extremely fun and addicting, and everyone that climbs at my gym tends to be supportive and not at all judgemental.

Hang in there, and consider trying crack or face climbing. One of the best wall climbers I ever had the privilege of following around was overweight (despite playing soccer and running and everything else). He couldn't boulder for crap but he had great balance and body english.

Obesity and climbing are a tough combination. I would recommend trying indoor climbing at first and working on routes that don't overhang (wall is <= 90 deg from the angle of the floor). If you work this in with a routine like cycling/runnning/swimming and a proper diet (start eating less carbs unless you plan on working out within the next couple of hours), you can develop a body built for climbing while picking up proper technique at the early stages.

Source: I've been climbing for 6 years