There is nothing so satisfying as "making it yourself", especially when you have the support that comes with "personal capabilities". Sounds like you do.
What you're describing can be done very lightweight. No matter how small (and lightweight) you make it, it will always feel heavier than you wanted (I may be reaching on that one, but it's a point to think on).
Without water, sinks, tanks, etc., weight can be nicely controlled.
I'd suggest (with your contractor, stick-built thinking) 1 by 2 framing laid flat. You might consider examining a little of our
chapter on our small camper structural framing thoughts. Sorry for the missing pictures, but all I can say is "photobucket", maybe you get it. And my lengthy detailed narratives without pictures might cause brain damage! So beware!
Even using a 1 by 3 on edge or a 2 by 2, would be overkill on a small lightweight house (camper), and the extra inch won't gain noticeable insulation affect, but will add to weight and/or cost.
With small R values (less than a 2 by 6 house wall) your main target is to remove "drafts" completely. Make certain your venting is proper for whatever heater design you choose (more a factor for radiant heat like a Wave 3 or 6 than it is for a basic forced air furnace, which requires both propane and 12 volt electric), but even with proper venting, simply keeping the heater on throughout the user experience will keep the interior comfortable warm when you need it. A 1 by 2 wall will hold your interior panel and exterior board just fine. I'd keep the exterior board just as thin as possible for whatever the fiberglass treatment needs. And Fiber glass will add some weight, which you'll be mitigating with absence of appliances and tanks, etc.
Build it! You got this! Target lightweight at every turn, and put your chosen floor plan and needs into reality! We did the same (although we've chosen more weight and greater luxury that you're planning), and we couldn't be happier.
P.S. I have a .pdf file for each of my chapters, saved on my computer, which includes the pics. So if you MUST see photos, PM me and I'll fire off the .pdf to you so you can get the narrative and pictures together.