You will run faster if you lose some weight - imagine running with a ruc sac and then taking it off, that's the image I use to try and help me lose the last stone and a half.
I lost a load of weight, about 4 stone a couple of years ago and it made at least 4 mins per mile difference.
I think you need to break it down into smaller goals. Your ultimate goals of losing several stone and 6 mins per mile may be off putting whereas if you aim to run one of your miles a bit faster each week and set mini weight loss targets it might be more motivating.
Just to agree with what the others have said. Ive lost around a stone over the last year and my comfortable running pace in training has reduced by around a minute a mile........now to try and translate that into a few PBs this year............
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