Belly isn't the big issue, give a thin horse a big net of poor quality soaked hay & the chances are it will have a belly. However while I can't condition score from a photo I would say from that photo he is quite fat - cresty neck even for a cob, no real definition between neck & shoulder, gutter along spine.
I wouldn't want to jump him a lot at that weight as he will be putting extra strain on joints & soft tissue - hence why it isn't ideal to d a lot of jumping with heavy horses too - but I shouldn't think some small jumps on good ground or a good surface will be the end of the world, he could put himself under as much strain gadding around in the field. Be sensible, keep working to get his weight down and monitor how he responds to his work - if he starts refusing or backing off his jumps, or looks sore the next day then ease off. If we never did anything with our horses unless they were the perfect weight then there would be a lot of horses doing nothing & it wouldn't be in their best interests.