Wow. Idiopathic means that they
don't know what is causing it. If your doctor is saying that loosing weight will stop it, he's misleading you.
That's not to say that you shouldn't loose weight, just that doing so might not reverse your symptoms/condition.
Now for some advice. I enjoy running outside, rather than on a treadmill, try getting a running app on your phone there are a whole host of options from zombies, run! Which is video game-styled one in which you are trying to out run zombies, pick up supplies and get back to base before you die/get infected to charity mile, which donates to a charity for every mile you run/walk. There are a ton of couch to 5k training apps you might want to try, most of them free.
Also, try finding other people to do things with, you might not get bored so quickly. Go out to a club and dance but don't drink (alcohol, water is very important). You'll get cardio exercise, hang out with your friend and probably have a ton of fun in the process. Also ask your doctor for suggestions (not your neurologist, your gp) Is it just actual weight training you should be avoiding, with high weights and the goal to gain muscle mass, or should you be avoiding high stress exercises. Ask questions, would body weight exercises be okay for you? Like push ups, squats, yoga, pilates, ect.(there are literally hundreds of no-equipment workouts on the internet, as well as videos, if you look on youtube) What steps can you take to avoid injury (going from not exercising at all to a lot of intense work outs can get you hurt, be careful and always stop if there is pain).
For healthy snacks, I like baby carrots, frozen peas (trust me, don't cook them, just eat them frozen from a bowl like candies, they are sweet and a great way too cool down), smoothies, which I make with greek yogurt (check to make sure they're not adding HFC or other questionable ingredients, I but a store brand because its cheaper and I've never had a problem) and fruit, and popcorn, if you have an air popper, the microwave stuff is horrible for you. And you know what, if you're willing to make it the old fashioned way on the stove with oil you could go that way, just try not to go overboard with butter. I always burn it when I try, so an air popper might be better, but you know, at this point, just try things and find out what you like that is healthy. You're much more likely to stick to it and make an actual long term change if you enjoy what you are doing.