I can understand your concerns, and it's good that you've raised them with your step daughter, who obviously realizes her son is overweight. However, unless she specifically asks for your help/advice, it's probably best to keep quiet about it.
The problem here kind of lies with your step daughter ... you say she seems to allow him to eat what he wants, and she can't force him to exercise, and he spends most of his free time on the computer. Frankly, I think that's a lame excuse for the parent of a child who must be, what, about 11/12 years old? She is responsible for buying his food, and putting it on his plate. And she is responsible for allowing him so much time on the computer. Understandably, during lockdown, children haven't been able to go out playing with friends, or enjoying sports, etc., but it sounds like this has been going on for a while longer than that.
One thing I will say is, please don't bring up this subject in front of your GS, and certainly do not mention about joining slimming clubs. Can you imagine what the idea of that would do to a child's mind. He'll end up having issues about diet/weight for the rest of his life.
As someone else mentioned, boys usually have a growth spurt around the time they start secondary school. I remember my own son was a bit chubby at that time but, all of a sudden, he became a slim, 6 foot teenager overnight!
You say you have a really good relationship with your step daughter. Do you every food shop with her? If you can, I'd suggest going with her, and maybe broach the subject about what GS likes to eat ... growing boys of that age do tend to eat rather a lot, but they need to eat the right things. If she's buying unhealthy stuff to keep in the house, then of course GS is going to eat them. But if she only has healthy stuff, then that's all he can eat!