weight gain is tackled mainly by diet. you can maintain a low weight without exercise if you have the mental discipline to stick to a low carb diet. carbs spike your insulin. when insulin levels are high food is stored as fat, when levels are low fat is burned. the keto diet is replacing carbs with healthy fats. this keeps your insulin from ever spiking so that your body is constantly burning fat and never storing it. if you want to mix in exercise(i have to since it helps with eating discipline) then you'll have to have one or two days per week where you do eat carbs to restore your glycogen(which is necessary for gains). keto also takes a lot of research to do properly. you need to take vitamins or otherwise find friendly sources of magnesium and potassium at least. if you want to get into it a good book is The Ketogenic Diet by Lyle McDonald. It's very dense but is probably the only book you'll ever need on it.
the gut is the first place that the body will store fat so it's naturally the last place you'll lose fat when shedding weight. maintaining a 500 calorie deficit with a keto or cyclical keto diet will get you shredded in a few months. the mental discipline required is very high though.
if like me exercise helps you maintain your diet discipline then i'd recommend either swimming or calisthenics. both can be done from the day someone comes out the womb to the day they die. swimming requires proper form to avoid rotator cuff issues and calisthenics requires patience and constantly listening to the body so as not to overdo anything. i would only recommend swimming if you plan to get proper lessons so that your form is tip top, and then to never swim so long that your form starts to slack.
form > distance.
form > speed.
as others have mentioned biking is good as there's no impact and is great for sustained high heart rate. biking does impose knee problems if you constantly break parallel and can exacerbate a hunched posture if you do it constantly.
i've found calisthenics(bodyweight fitness) to be more available since i don't need any equipment. in my opinion the healthiest exercises are static holds since there is literally no movement to aggravate the joints or cause repetitive strain injuries. calisthenics is full of progressions to always keep you busy and challenged but requires a lot of patience and consistency. for example you need strong wrists. to build strong wrists you have to very slightly break down the tendons in your wrists and give them extra time to heal. this can be done by performing push ups on the backs of your hands(obviously there are progressions to this). since tendons have much less blood flow than muscles they take much longer to repair. but once they heal they retain their new size for much much longer.
think yoga but with more and more challenging poses. yoga has the added bonus of stretching you out at the same time.
grip strength is also extremely important and beneficial to the body from better blood flow to overall better control of any exercise.
calisthenics can definitely impinge nerves and such if done incorrectly so stretching and form are paramount, but if you can master a full scorpion, a full planche, a front lever/back lever, a L/V sit, an iron cross on rings, 10+ dragon flags, a 10 minute+ dead hang(some fit nuts will probably chime in with a bunch of others) you'll be extremely in tune with your body and as a result have an amazing physique and cardiovascular system. obviously these are all the final stages of long progressions so please be patient with yourself and do constant reading on the subject to keep from hurting yourself.
ideally you want to have an elevated heart rate for at least 20 minutes at least three times a week. that's actually really easy with calisthenics since you can get creative with HIIT or circuits of your own.
the #bodyweight and #calisthenics filters on instagram can be good inspiration, sometimes they even have tutorials.
https://www.instagram.com/calisthenics.women/
https://www.instagram.com/explore/tags/calisthenics/?hl=en
https://www.instagram.com/explore/tags/bodyweight/?hl=en
some interesting people,
https://www.instagram.com/simonsterstrength/?hl=en
https://www.instagram.com/moderntarzan/?hl=en
and age is just a number, there's tons of videos of people 70+ doing things neither of us can do.