I think the stove you were looking at on amazon is not bad - its very economical. It is heavy but not crazily so. If you make your own pot cozies you should be in business. You may eventually rebel at the weight if you "catch the UL bug" but it might be a good place to start. I can think of a few non-weight issues, but nothing to harp on. There are loads of real experts on here, so they might have something more interesting to say about it.
Here is what I'm using at the moment (about 1/2 the weight, but probably a bit more than twice the initial expenditure). I spent a lot of time thinking about it as a complete system, but I'm sure it is nearly identical to what a number of people here use. I have used a mini canister stove for most of my "career" but wanted to put together something more adaptable as well as less ecologically wasteful without the used canisters. Full disclosure, I still have limited actual experience using this system by comparison, but I like it a lot already.
The criteria I tried to integrate were (0) matching windscreen (goes without saying), (1) light as possible, (2) pot sized large enough, with room to spare, for nearly all "2-person" size dehydrated meals when cooked and eaten IN the pot, (3) multi-fuel options including wood for "emergencies", (4) good fuel efficiency as well as the ability to recover unspent fuel if desired, (5) pot cosy for keeping food warmed, but more importantly for performing jobs that are typically done by simmering (e.g. rice, pasta) by boiling water, sealing up tight, and waiting for long enough. Lastly (6 - the hard one, for me at least) I wanted to have it all fit inside the pot in a neat single package.
I can say if I also intended to do the above AND to share with others my head would have exploded. To do all the above AND share with others you may end up having to serially boil water for them. If you don't care about time then it will be fine, but that can be said for any stove setup. If you want to just boil a big honkin' load of water quickly and share then maybe go with a Jetboil. On the other hand, everything below is built around the pot. You could size up to the 1.3L Evernew pot (or another larger pot) and matching Tri-Ti and then you could probably "cook" for 2-3 people.
As mentioned above, with a creatively used good-quality pot cosy you can perform a wider variety of cooking tasks than re-hydration (e.g. making pasta, rice, and so on), though of course not everything. Simmering is not easy, but possibly unnecessary if you use a pot cosy creatively. So there is that part of your criteria - you will have more cooking options that just re-hydration. Plus in the system described below you can use alcohol (my preference), esbit with only a tiny 3 gm (I think) additional hit for adding a gram cracker, and wood in a pinch, all quite efficiently. I thought a long time about esbit and finally decided because of the smell and residue I would not use it with this system unless I had no other options, just Alcohol with the option of using wood if I somehow ran out of fuel, or to use wood to extend the range of my fuel when using found wood was possible (and legal).
Here is what I came up with. It is mostly intended as food for thought. Maybe it will help you figure a few things out you will like, and that fit your needs.
Total package (7.2 oz):
Contents - Evernew 0.9L Ti pot w/handles removed, matching Tri-Ti sidewinder stove, tyvek, storage envelope, 12-10 Alcohol stove (last 3 all from trail designs, and you could add the gram cracker that comes with the set for esbit if desired), Ti tent stakes for wood use with Tri-Ti(not shown - multi-use,in my stake bag), homemade pot cosy, potgragger (I use this instead of the original handles because I need it to ALSO grab the windscreen and move it while hot in order to snuff out the stove and retrieved the remaining Alcohol, if any.), Ti spoon, cut-down lexan fork, foil snuffer, plastic bag for stove to keep any fuel residue out of pot, cuben stuff sack:
"In Use" config (OK, should have had lid on as well):
With DIY Pot Cosy (refletix and reflectix tape), not sure the lid cosy will make a huge difference here LOL:
Add fuel bottle of choice (or esbit sealed in a bag). A small one can be stored in the pot (inside the sidewinder) but to my mind not really a good idea. I keep all the fuel separate, and double bagged, in my pack.