Try including avocados in your diet and hemp. (avocado does the brain good) I have found them to be far superior to egss for protein but if you choose a non vegan source for protein then eggs would be best in that domain in my opinion.
If your vegetarian diet is cooked and deplete of minerals and calories (ie lacking organic produce and plenty of fruit) then I can see why you could loose weight and feel lousy. This is a big mistake many attempting Vegetarian or vegan make. There are other pitfalls as well. Many don't eat near enough fruit or way too much fat.
"Vegetarian protein is less usable and what aminos it does have is less usable by the body."
Not from my personal experience or research on this topic. Not by a long shot.
The bottom line is the body has to break down the various forms of protein whether it be from plant or animal origin and our digestive systems are much more geared for plant matter assimilation, without the added stress of putrification etc.
Then the body uses energy to assemble human protein. Because of an easier assimilation and less energy expended on plant digestion, this leaves more energy to do other things , like assemble human proteins.
Speaking of brain fuel...Einstein was a vegetarian. ;-)