It's tricky.
My son was fat. I got it in the neck all the time from the ped. From the time he was three months old she wanted him drinking baby tea as a sub for milk for three feeds per day. Aside from being culturally allergic to giving a baby anything called tea, my son point blank refused to suck on any nipple that wasn't made of skin, so the idea of putting baby on a diet was a non starter. He stayed fat until he was a jumbo sized 2 and half year old (girthwise).
And then he slimmed down. I wasn't feeding him less or differently, just all his baby fat fell off as he started to grow upward at a cracking rate.
People who only saw him eating when we had company would probably have been under the impression that we fed him exclusively on fish fingers. But I am a rotten cook and hostess, so my fish finger standby was easy to fit in around cooking for adults and meant that perfect parents (i.e. the people who don't have any children yet) couldn't tut at me as my son got some kind of cosmic signal that right now was the perfect time to act like vegetable were venomous and he should kick up the most public fuss possible.
So I don't know. Because it is hard to say to what extent your impression of the situation is the whole picture or snapshots of bits here and there. How much time do you spend with her ?
Even if it is as you think it is, I not sure that there is anything anybody can do in terms of intervention until things reach a truly gargantuan state of a affairs.
So in the interim, maybe offering a sympathetic ear and shoulder to try and see if there are underlying issues (of maternal confidence, depression, child's sleep issues so she stuffs with food to try and get him to sleep so she can too)...and help her deal with those, so at least you don't feel powerless ?
Although..I'm wondering if there is a way of exploiting the "genetic" explanation by saying that the kid needs to be tested for them cos there are issues connected to that which need to be addressed asap. And using that as a backdoor way of getting her to bring his weight issue to the attention of the healthcare system. Maybe then having to confront the issues she is creating for him if in fact the quacks say he DOESN'T have genetic issues and his diet really isn't up to scratch.
But from the sounds of it there is no way you could persuade her to bring up the issue with the doc anyway, so that probably won't work.