I'd text back "sorry, Fat Club was very helpful to me, I see now you're too good for it"
Wow, that's harsh, really harsh, clearly she's not saying she's too good for fat club, she's saying she didn't realise she needed to go.
Personally if a friend whinges to me about putting on weight, my immediate go to response is you look fine, only if and when they say they want to do something about it would I be supportive. So for example if she said, I want to join weight watchers, then I'd have said I'll come too.
I wouldn't sit with a friend who'd just had a baby and was whinging about pregnancy weight and immediately jump in with go to fat club. Some times people just want a whinge, they don't want you to confirm that yes indeed they are fat and need to do something about it.
Suspect the op is right when she says she thinks she jumped in prematurely with the suggestion.
A woman who has just had a baby, saying she's out on weight, seldom will meet the response of, yeah you're right, you should join fat club, with gratitude.