Have you considered one of these liquid fuel stove? I mean if weight and money is the issue the Vargo Triad weight 1oz and cost 30 bucks! Of course you still have to carry around fuel but since gasoline is readily available you can just carry enough for a couple meals. It works with fuel tabs too.
But if you really don't want to carry any stove, you'll have to buy food as you go. In the middle-east, without a stove, this is the food you'll probably eat or see a lot: of course you'll drink liters of tea (offered every time you stop), pita (flat bread), melon, peaches, dates, pistachios, cookies. In restaurant: kebab, shwarma, falafel, (you can buy the balls and carry them with you they stay good for a day or two), eggplant.
You might want to consider a thermal bag to carry your food safely. There is some travel one out there that are very light. That would allow you to carry stuff like milk, yogurt, borek (pastry with cheese or meat filling that ou find in Turkey) etc through out the day. Middle east is all about meat so I think you didn't pick the best destination to go for veggies but I don't think it's a stupid idea. I know a lot of people who traveled without a stove (usually on shorter trip though) and there is usually enough food available.
Bread will be your best friend, dates are excellent over there, and as you said you'll be invited all the time and most likely you'll be leaving your host with some food they gave you.
When you're abe to, you can cook some pasta or rice and carry them with you. They won't go bad for a while even if they are not refrigerated. Then just add mayo (mayo can also be carried under the sun for days - scarry but true!), a can of tuna or a can of chicken, tomatoes, veggies and whatever and you got a good meal. Canned sardines are handy too. Any canned food as a matter of fact. I've eaten cold beans or cold ravioli... when you're hungry everything taste good!