I recommend that you consume easily digested protein such as pea protein powder which is fairly cheap and can be mixed with water. The texture is fairly nice and smooth and the taste is tolerable but that could be spruced up with something. I have started adding FOS to sweeten it. I also take it mixed with some Rice protein but that stuff is pretty terrible texture wise because the powder can be "tasted" even though it is very fine is still tastes chalky. However when mixed with Pea protein it makes the protein quality very high. I can digest this Pea/Rice very quickly, unbelievably so because earlier 47g Pea and 15g Rice was out of my stomach in less than an hour. Those are both 80% protein powders so lots of protein which you are probably lacking. I recommend that you get some pancreatin as well, I use the now foods capsules which helps a lot. Improving your digestion of protein and increasing your protein intake and digestion might help you increase your weight. Don't be afraid of getting some fats such as Omega 3 and VCO. My protein digestion was so poor that my skin would not heal or form scabs. Since I have taken protein powders such as Pea/Rice and Whey my skin heals much better.
Even better would be hydrolyzed protein which is pre-digested so you get the amino acids directly and your body could not react to that. It is a lot more expensive which is why I do not do it. Until I have sorted it out I will stick with Pea protein and Rice protein because it is so quick and easy to digest. I will stop whey as soon as it runs out. It is far more difficult and slow to digest, tonight was a deciding factor for me.
Because you react to foods and are clearly allergic, which you would be because the cause maintains the permeability for a reason, have you tested your stomach acid levels? I bet you have little active stomach acid. Probably high histamine levels too. If you do have SIBO then low stomach acid levels are almost certain because it keeps the stomach sterile and most bacteria are destroyed, except for some that might get through when the acid levels are not so high. Unfortunately that is when the problems begin!
Eat only easily digested protein such as Pea and Rice first thing, you can have some fat with that but no carbs and do not eat or drink until it is out of your stomach! Take some pancreatin with it to speed digestion which will help digest the protein and fat. Then have carbs such as fruit and veg but no protein foods. Have another protein meal after that has digested and cleared your stomach. I understand what is happening better than anyone else on this. I know the cause of the hyper permeability, how it works and what it does. I am attempting to get what is needed to destroy it but I am finding it difficult purchasing what I need to complete that. I am about to try china because I am fed up waiting on this, it's very frustrating knowing and being prevented from eliminating it.