I started my journey the wrong side of 24 stone, so weight was a consideration for me, I went for a BSO from
ebay, (see my avatar) which did me for over a year, never broke spokes in the 3200 miles I rode it last year. I've lost a lot in the past 31/2 years I've been cycling regularly. It's easier and more fun that any kind of diet/gym.
One thing I'll say, a fast bike will not make you faster, only you can do that. I've gone from 55 minutes to do 8.5 miles to 28 minutes to do 9 miles all on heavy cheap MTBs and even cheaper hybrid. Only the motor, (me) has changed