Hi! I'm recently married and new here as well! Haha your cat sounds like one of mine. :) We bought a harness and leash for our cat to see if we would be able to walk him...yeeeeeah....he ends up just laying on his side and becoming dead weight and he will just let him drag him. LOL. So much for that. I guess I was ok with that because I honestly would have felt a little silly about walking my cat. I think some people do but I don't think it's necessary.
Both of our cats are strictly indoor cats. We don't really do anything special with them for them to get exercise. Just buy some toys...my cats love things that have strings. My cats love ones with sticks that have feathers or strings dangling from it. One of mine loves soft little ball toys too. He used to play fetch with us when he was younger. Now that he is older, he doesn't do that so much anymore. Also, they will randomly run around and jump on things if they feel the need to get some energy out. Not sure if getting another cat is an option for you but ours seem to keep each other entertained .I think having another cat around to play with gives them some exercise on their own.
You could also try getting one of those big cat house things that have multiple levels to them so he can jump around on it and such.
In general, I think cats are just really lazy. I don't think they require the same amount of exercise as a dog would. Not to say they don't need exercise, but I think some toys and some portion control with his food is really all he needs to prevent an overweight cat. Our cats used to be way more playful when they were younger, but as they got older, they just mellowed out a lot more and do what cats usually do: sleep. :)