What do I need to know about math/physics/mechanical engineering/cad/fabrication to learn how to design and build bicycles?

Look at current bikes.  Find books on Statics to design the frame.  You will have to figure out where to get the metal tubes, and what the diameter/wall thicknesses you can buy.  Notice where the seat, handlebars, and  pedals are relative to a rider's body for ergonomics.  Seat and pedal location play into stress analysis of the frame. Look up books on gears to figure out gear ratios and crank lengths.  Bike magazines also have good tips on gears.

If you are going to stick with steel and aluminum, you might want to study the Nishiki, Bianchi, and Ross 290 series (but no other Ross) from the 80s and 90s. They are light-ish (for the materials of the time), but quite strong and stable bikes. The designs are classic and there's still a lot of them out there. I have a Ross 292 for my daily commute to the train station. The other nice thing is, I don't really have to worry about it being stolen as compared to modern $1000 bikes, but it still rides very nicely. You're going to have to think about control of the bike: stiffness and or softness, overall ride quality, and stability, as well as effort required to make it go.

I suspect that most custom bike makers are not engineers.  If you are working in metals, then it may be worth it to learn statics, dynamics, strength of materials, CAD and finite element analysis.  All of this is a crazy amount to learn as self study.  I suspect that you could get most of it from a community college, though.  That said, the most important thing by far is to learn about how to set up and run a successful business.  Also, learn how to process orders effectively.  The bike companies that impress me the most are Seven, Strong and Breadwinner.  If you are in the Boston area, get a tour of Seven.  They have managed to get the manufacturing of amazing custom frames to a science.  As an engineer and owner of a Seven, I am impressed.  Strong is an example of a solo builder who has figured out how to make a decent living off custom bikes by being super efficient in all phases of the work.  Breadwinner is interesting to me because they have gone from true custom to....well look at their website. Personally, I'd look at getting a job at Seven or similar place and take night classes in areas you are interested in.  Seven is interesting because a number of their employees also have bike companies on the side (like Royal H).  As far as what to read, I suspect your classes have introduced you to a lot of it, but I've always liked Bicycling Science by David Gordon Wilson and the Bicycle Wheel by Jobst Brandt.   I imagine you are already familiar with BikeCAD, but you might also want to look at learning a more general CAD package like Solidworks.  I'd suggest learning a CAD package with some level of integrated finite element stress analysis built in.  Given that you will be designing specifically for heavy people, BikeCAD probably won't do everything you need.  The other thing that would be worth learning is how to use strain gauges and telemetry to look at the frame stresses real time as a person rides.  Finite element analysis is great if you know the loads to input, but testing your creations will help to improve them.

Surprisingly, it's still something of a physics mystery how bicycles actually work, so an engineering class might 'over educate' you.  Cycling is also fairly traditional, so designing a bike from first principles might also work against you - you'll end up with something so weird, no-one will want it regardless of how well it works. My advice?  Learn about composites.  If you can build custom carbon-fibre frames, you'll have a market. If you're going to stick with metals - the two or three years in school would be better spent learning and refining practical skills.  You have a specific skill you want to learn - concentrate on that.  Spend two or three years building bikes, and becoming an expert welder.  Get aerospace grade or oil and gas industry weld certification. (if nothing else you'll have a guaranteed income from that - it's very well paid and highly skilled)  Learn gas, TIG, MIG, and so on. As for obese bike riders - are there any?  And why can't they ride normal bikes?