Hopefully this adds something different. As a previously very overweight guy that did something similar, here's my 2p worth. I ended up working with some Ironman and Ultra winners during my training so some of this is their advice too.

This may be counterintuitive at first but hill and speed work helped me more than solely focussing and worrying about distance - that will come without you realising. I was doing hill reps or speed work on a Wednesday, with a fast (timed, so push yourself each week!) 5k on a Saturday morning. I did this religiously and then started adding in an easier longer run (anywhere up to 10k) on a Monday or Friday. You'll find that you'll surprise yourself on the longer runs each week - this is where your distance improves without you even worrying about it or noticing it.

Don't just mile binge or focus on mileage increase. Sure it'll help mentally to know you can get there but focus on the general quality of your running. Consistency, quality and weight loss are what you should be aiming for rather than 'I need to add a mille on a month' etc. The fitter and lighter you get, the longer you will naturally go for.

Being overweight, I can't recommend this bit enough. Get into a gym or if that's an issue, google some core strength and leg exercises that you can do at home. Pilates or yoga type classes are excellent. I went from 0 to 1/2 marathon in about 6 months and then another 6 months to an Ultra trail and ended up with back issues from increased stress of the extra weight and impact. The core strength will make you stronger on your longer runs in holding your body upright and will hopefully keep any injury at bay - the last thing you want is to put all your hard work in and then come away injured just before your big day. These exercises aren't just for injury though, strength work will also make you fitter, burn fat (increased metabolism - weight loss etc) and you'll feel better about yourself, trust me!

And good luck, you'll smash it!