Size of instance after reduction
First of all, for your definition of NP-complete, we require the reduction to be polynomial time. This makes it so that if we could solve an NP-complete language, L, in polynomial time, we would have a polynomial time algorithm for all of NP by composing the polynomial time reduction with that algorithm for L. 

Note that the size of the output of a reduction has to be less than the run time of the reduction. The biggest output possible given a fixed run time would be one where a Turing machine, M, prints to its output tape at every step.