I think you were right in what you were thinking, but your comments were doomed to fail. You've pointed out, rightly, that these folks are in the "blame game" and the "poor poor pitiful me" phase. I think, as hard as it is, you have to let it go. You don't have to comment on her photos (and if she asks, you can say you didn't think a comment was required (or even that you missed it). Let it go.
Look, I totally sympathize with you and I know that you are worried about them and their son. I work in food science, and I can tell you that 99% of the time, people comment about their poor health or their poor finances within about 5 minutes of any conversation. I spent a lot of time in the beginning "wanting it more for them than they want it for themselves" - I jumped in to be helpful and supportive, when all some people want to do is complain. Sometimes they just feel overwhelmed and powerless, sometimes they blame it on "bad genetics" (when science has shown that it's really based on poor epigenetics which means it can be changed/reversed), sometimes they're in complete denial.
You didn't say anything about her weight, but focused more on the diabetes. Fine. But it's all part and parcel of the same thing. She does not want you to be right. She does not want to take responsibility. She does not want you to tell her how to be a better parent (by getting her child to focus on better choices or whatever). I think the fact that the comments were public on Facebook may have made a difference. But we certainly see that attitude even here on an anonymous site like Mamapedia - a lot of people post because they want us to agree with them, and they get ticked off if we don't.
So here's what I do: the first time they complain or express worry, I say, "I am involved in something you really should take a look at. There are plenty of others with similar issues who will help you." The second time they complain, I say, "Remember that I have something that will help." The third time, I find a nice way to say "I'm not sure why you are telling me this, because you haven't responded to anything I've said before. I cannot help you if you are not open." Then I change the subject or I walk away (with a nonchalant smile) to take a (fake) phone call.
Sometimes people just don't want your help. You have to accept that about them. You don't have to enable the behavior by commenting on how delicious this lunch-for-three looked. You don't have to answer her comments about being a bad friend. You don't have to say anything.
If she asks, you can say you are sorry you posted publicly about something she didn't want to hear. And everyone else saying "oh that's awesome" was definitely a form of enabling her - which is why she posted to begin with, to get permission to continue. So you don't have to enable, but you can't expect to change the others any more than you can change her or her husband.
Now, are they going to die young? Yes. Are your insurance rates higher because people like them engage in highly risky behaviors? Yes. Are your insurance rates higher because people who don't have preventive care wind up using the ER for every sore throat? Yes. Are you going to solve this on Facebook or in your regular life? No. All you can do is draw a line in the sand and, IF ASKED, say, "I won't help you die." But that's going to tick her off too. All you can control is your own behavior - so that means not having big all-you-can-eat BBQs or the like. But you can't give her the idea that you think it's okay for others to have big lunches but not her - I'm sure you don't think that, but it's often how sick people respond to "deprivation."
If she's a real friend, she will miss your contact and come talk to you about it. If she's not, then you haven't lost as much as you think you have. You should surround yourself with people who want to get healthy, join the walking club, share healthy recipes, and so on. The hardest thing I've ever done is watch people I care about decline in health when something very simple could be done that actually requires not so much willpower. I've decided to focus my energies on people who are OPEN to my expertise and not keep trying to sell it to someone who's just not buying.