I find this a frustrating topic as there are so many different regimes and types of HRT and I have never been able to find info on different sorts. People on here (and the net advice in general) will say no it doesn't affect anything, menopause itself does. However, for me, when I was on one regime I found I was uncontrollably hungry for parts of it. Just uncontrollably. The net will say oh it doesn't affect weight, just appetite. But FFS one affects the other, no? The kind of hunger I had was just torturous. I'm not any kind of control freak about weight. I'm overweight and have to struggle not to put more on (never much acknowledged by our society), so I don't want to make things even harder.
So I suspect that it can affect weight but it might depend on the individual and finding the right regime for each individual. The more i ask others about HRT the more I realise that the way my body responds is quite individual as well as general. The effects I had above, some of my friends didn't at all. But I do know that since swapping regimes, the mad hunger phase went along with some other side effects I was having. For me, it was worth persevering to find the best type and regime for me.
It did redistribute the fat a bit too. So my diminishing bottom before HRT (which I had been quite pleased about) returned full force. However, I also rediscovered more waist,and I read that carrying more weight on the hips and less around the waist is (hopefully) better for health so I'll take that. But I'm just mentioning this as clothes might change in how they fit giving an impression of this or that. You say you've put on weight but not where you've put it on.
People tend to talk on here about HRT versus non HRT and lump all the types and regimes of HRT in together. But it's not just a case of one type of HRT or no HRT. If an HRT doesn't suit, but helps a lot of other things, there is the option to try another type or regime. That said, it can take the body a while to adjust so it can be worth seeing if things settle down or if the body gets used to any particular regime first.