Do graduate schools increase assistantship stipends if the student is accompanied by a spouse or dependent?
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.