I've continually been what the experts call "over weight". I had the discipline, but not the inclination, to get down below (my lowest since high school was about 200 and I'm 5'8"). But I would do physical labor around the house to keep in shape and I usually was in better shape than I looked.
In the last couple years I've felt the same sort of feelings you have in terms of having "life crap". I've just got a lot of things going on. The typical childhood problems - how to get your kid to baseball, teaching your kid he can't call other kids "dickheads" in class - pale in comparison to the life problems they have when they get older. You have your issues, well documented, and I have, if not the same then ballpark similar ones. And for me, it's draining mentally, and saps that energy that I would use to go out and split wood or some other activity that I consider "my exercise".
This past weekend I did something I have never done EVER in my life: Every house I've owned (four or five now) I go in and paint, most if not all of the rooms. If the house is over 10 years old, I change out all the outlets and switches. A cheap way of making the house look "clean" and "new". ALWAYS it was "I'm able, I know how to paint (I do) and I can do this myself". Well, I paid a guy to paint my bathroom this weekend, and I will likely be paying him to paint my hallway and staircase. It's a big deal to me, though it may not be to others, but I kind of think it's in the same ballpark as your "inertia" about losing weight. Don't beat yourself up; we have capacities, and outside of an emergency or a life or death situation, those capacities are finite. I'm not suggesting you let your health go, but you do have to decide where your capacity is best served. My wife finally convinced me that taking care of my parents and my kids is more important than painting a bathroom, and I agree.
Something to consider.