Is it legal for my employer to average hours I work over two weeks?

A: No.  If you work 30 hours one week and 50 hours then next, your employer can not avoid paying you overtime by writing you one check for 80 hours at your regular rate.  Instead, your employer must pay you for 10 hours of overtime pay (one and one-half your regular hourly rate) in the week you worked 50 hours.   "Averaging" is one of the oldest overtime scams used by employers.