Can't help much more than your self disciple can.

You must help you yourself first, before anything.
And at least, some push-ups and sit-ups won't hurt, I think...

Most people give up after about a month
You could get a buddy to train with you which means the incentive of not looking like an a** by bailing out might be enough to keep you going.

Martial arts teach discipline.

And only through discipline will you stick to a diet.

Cost? f*** son, you can take just one boxing lesson and just stick to those exercises they teach you. I'm not asking you to go pro or become the grandmaster or some s*** like that.