Great questions @arthur.t , although the answers aren't always simple.
As you suggest, you would want to account for inflation and market size. While there is no single way to do this, sometimes scaling all the variables makes sense. One usually wants to deflate all dollar figures. So instead of dollars use dollars divided by a price index such as the consumer price index.
Market size is harder. Sometimes one divides quantities by market size (perhaps population, perhaps something else). This makes sense for modeling individual behavior, but might miss out on what happens when the whole market grows. So one might scale by market size and then include a separate market size variable.
Weak instruments aren't likely to be worse than least squares, but if they are really weak they won't be much better either. (I can say this because together with a colleague, Charles Nelson, I'm the person who discovered the problem of weak instruments.)