While the accepted answer gives a lot of examples, most of them are somewhere between difficult and impossible to weaponize at your tech level, or would simply not work.
- Falling, mines, car bombs, trap doors, extreme pressure, slow squashing, and tearing apart all use kinetic energy to kill so they don't apply.
- Poisoned needles, drowning, burying, hanging, tying up, and rolling up in a carpet are practically impossible to inflict against a person of superhuman toughness and reflexes.
- Poison gas, poison (ingested?), hunger, dehydration, and acid would require trapping the BBG in some sort of way which may be doable, but is still a poor vector for weaponization, especially with his reflexes since he could so easily leap out through a slamming door or what not that you try to capture him with. And even if you do trap him in a room and try to stave him out. He can just punch the wall a few hundred times to build up power for a super punch to break his way out with; so, any trap you do use needs to kill quickly, and close off faster than he can get out.
- Vacuum, freezing, microwaves, lasers, and radiation don't fit the setting's tech level. Electrical weapons (like cattle prods) and biological weapons (like small pox blankets) existed, but there were not good delivery systems to weaponize them yet.
- Extortion, cut tires, and SWATing are more of annoyances than actual ways to beat the BBG.
- This really only leaves burning, which with your tech level, there were some pretty effective weaponization options. Most notably, the flamethrower.
Flamethrowers have minimal kinetic energy to exploit, but LOTs of thermal energy and asphyxiating smoke. Sure, he could stop the stream of burning fuel on contact... but then he's covered in sticky, choking, burning fuel and will be very dead very quickly anyway. His reaction speed is also not very helpful since the weapon spreads out with range, even if he starts to get out of the way, it wont be by enough to escape harm.
But isn't Thermal Energy just Kinetic Energy at a very small scale?
Technically this is sort of true, but effically it won't make much difference in this case. While I don't think the OP intends for his BBG to be able to absorb heat since that would open up a whole new set of super powers, even if he could, it would not actually save him from a flame thrower because the BBG needs to make physical contact with something to absorb its energy.
When hit with a flame thrower, it is not the liquid gas touching your skin that burns you, but the vapors coming off of it, mixing in the air, and igniting around you. So, while he could maybe absorb the convective heat reaching him through the burning fuel, there would still be more than enough radiant heat to maintain the chemical reaction and cook him alive... and even if he could somehow shield himself from all of the heat, the flamethrower would still burn up all the air around him and replace it with a choking cloud of smoke.
While this guy may exploit his powers for infinite stamina under normal circumstances, it means his actual lungs are going to be about as good as those of someone in a wheelchair since he never pushes them past thier resting workload; so, things that deprive him of air will have a quick and profound effect on him compared to a person in normal health.