Hi Joe, I thought I'd reply without looking at what others have said to you, as I want to give you my unadulterated views...
Firstly, I think that the most important issue is how motivated you are to do it - more than any physical preparation, it will be your level of desire to keep going that will determine your success. That's probably more true if you are unfit and physically unprepared.
Secondly, if you go and are unfit, then don't be unrealistic about what you can achieve on a day to day basis. Don't try to walk further than you can. You will get fitter, the longer you walk.
Lastly, there is a mountain of practical advice on this forum - have a look around and take from it what you think might work for you and what you think you're comfortable with, and disregard the rest. There are lots of different opinions on how to go about this gargantuan task, many of which are presented as facts - in my opinion, everybody has to figure out their own
best way to tackle this beast - and you should be prepared to revise your approach in an ongoing fashion, based on how things work out for you along the way. Some examples - there is no one "Camino" - the "Camino" doesn't start in SJPDP - you could equally start a few weeks further back from somewhere in France, or you could start in Roncesvalles or Pamplona - both good options for somebody who is unfit and feels less well physically prepared that they'd like to be, and doesn't want to start on day one with a massive hill! Or you could walk a different path altogether to the
Camino Frances - there are many choices. Another example of an opinion which should, in my view, be critically assessed, is one which has the camino broken into "stages". Guidebook writers created the "stages" - there are lots of other places to stop or start, and you will probably feel more comfortable walking shorter days, at least in the beginning.
In terms of practical advice - I'm sure others have said much of this already, but the following are a few things I'd consider doing - things that worked for me: get some light weight shoes to walk in and break them in before starting; use walking poles - they will save your knees and make downhill and uphill sections much easier (YouTube can show you how); take as little as possible with you, you only need one change of clothing plus what you're wearing. That's just what worked for me though!
It sounds like the Camino might be a good thing for you Joe - have fun, and enjoy the people you meet along the way - its a beautiful experience! I'd love to hear how you got along afterwards.
. Not my problem if you need to limit yourself.
. We don't have mountain bikes so tend to keep to the roads rather than the path - experience of that can be a challenge in itself! 
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. I walked the Camino Ingles because I had limited time like you. The weight won't hinder you as long as you listen to your body: Walk when its good to walk and rest when its good to rest. I met and walked with a lot of people but when the uphill's came along I slowed down and they moved on. And it was OK. PS I don't know about your route but I didn't loose any weight and I was not planning on it for such a short Camino. I also wanted to enjoy some of the Galician food (and beer).
