Unless you are an exempt employee, or work in certain "protected" industries,and it does not look as if you are, you should be paid overtime for any time worked over 40 hours in any given work week. Using your example, you would be entitled to 10 hours of overtime pay in the first week regardless of how many hours you work in the second week. Your situation involves important and complicated matters of law and fact. I urge you to consult with a lawyer on this matter.
The first question is this: are you an employee of this employer? If the employer withholds payroll taxes and issues you a W-2 after the end of a calendar year, he has acknowledged you are his employee.
Are you an exempt employee? Employees in some postions are not entitled to overtime pay becasue under federal and applicable state law, they are "exempt" from such entitlement. However, it appears that your employer is not saying you are an exempt employee, only that you have not worked 80 hours in a two week period.
As a non-exempt employee, you are entitled to be paid 11/2 times your regular straight-time hurly rate for all hours you work over forty (40) in a workweek. This is true regardless of whether you are considered a seasonal employee, temporary employee, full-time employee or any other status.
Since you are on a two-week pay period, you could request time off during the second week in lieu of overtime pay for the extra work during week one. Time off in the second week would have to be given at the rate of 1.5 times the hours you worked over forty in the first week, and the option to receive time off in lieu of pay is soley your option---your employer has no authority to give time in lieu of pay absent your specific request.
You are owed back wages. If your employer will not pay-up, I suggest you see an attorney.