If your due date is July 16, then your due date is July 16.
This is how it works:
Women menstruate. This is the begining of the cycle. First day of your period is the first day of your cycle.
If you have a 'perfect' 28 day cycle, you ovulate right in the middle of the cycle - or 2 weeks after the first day of your cycle. By the time your period is late, you are considered to be 4 weeks pregnant even though you only ovulated 2 weeks ago.
You get the 'bonus' two weeks added on. Really this is just done for dating purposes. This is how pregnancies are dated, how due dates are estimated, etc.
You don't need to add on 2 weeks to anything because it has already been done for you.