If you don't have expertise in physics, Weinberg is extremely difficult to read---he uses notations that nobody else does, and its full of technicalities.
A much more approachable first text for QFT is the book by Zee.
Weinberg is pretty good. I also like Schwartz's new book, though I'm biased because I took his QFT class. The other book I really like is Peskin and Schroeder.
You should probably have at least a good understanding of non-relativistic QM and special relativity. For the math parts a little bit of complex analysis helps, but any good book will explain the relevant parts.
A much more approachable first text for QFT is the book by Zee.