Usually a TA stipend is only given to cover the expenses of a single student. I have received a stipend of about $19000 for 2 semesters (9 months) and a summer fellowship ($4000). Is it appropriate to ask for an increase even before I go to graduate school as I have to fund my spouse (I am an international student)? Or is it better to work for a semester or two, perform well, build a case and then ask for an increase?
No, the stipends are set according to uniform rules for the department. You will not get extra if you have to support a family, although there are probably other, non-financial, supports that the university will offer your dependents (such as married student housing). Moreover, TA pay is not typically subject to merit-based raises either. You will not get a raise by asking for one; your stipend may go up slightly when you reach a major milestone (such as qualifying for the Ph.D. program), but mostly it will rise at the same rate as all the other TA's.