Funny, I'm 56 and my doc said my bad knee is like that of a 70-year-old.
I had a very bad knee injury in 1990 - total knee dislocation (not just the kneecap). I was in rehab for 5 months and a full leg brace 24x7 for a year. The joint still has limited range of motion and is full of scar tissue and bone spurs. My good leg is 50% stronger on a 1-legged leg press.
That said, I lost ~100 pounds starting swim workouts with a local Masters swim team. Competition was a great motivator for me.
I realize OP will not find this a good solution; but I really would like to encourage private or semi-private swim lessons. Another thought: swim fins really help sinkers and they are fun. Snorkels are favored by some. Even elite competitive swimmers use these during training in certain conditions.
I also did weight lifting and calisthenics to improve overall strength.
Then I lapsed, regained all those pounds and more ...
I did get back to regular swimming and was more careful with my diet and lost ~100 pounds. I still have many more to go.
But after a brain surgery and a week in ICU, I was ordered to walk 1-2 miles a day for exercise and my knee could not tolerate it. No other forms of exercise were allowed, nor was I permitted to ride in a car for a while.
I decided that swimming wasn't enough to stabilize my knee and as soon as the doc allowed it, I took up cycling.
It was a long haul. My first rides were measured in blocks, not miles. 10mph on flats would about kill me. The smallest incline redlined me.
Four years later, my bad knee is the strongest it has been in 22 years. My weight is still a problem but my power-to-weight has improved so the hills are easier and I go faster on the flatter terrain and into headwinds.
I still avoid walking for exercise and cannot do anything with jerky or unpredictable motions. No dancing, bowling, stair climbers. Nothing where I kneel or put weight on the front of my knees.
But swimming and cycling are both great for bad knees and for overweight people.
My next sport might be some form of rowing. I'm intrigued and think it would be forgiving of my situation and might play to my strengths. But now I'm just having too much fun on the bike.
If riding fast isn't your thing, you may enjoy riding on bike trails with a hardpack (unpaved) surface on wider tires.