what's the difference between simulated and measured results? 

Its better if you can provide the Comparison plot and a picture of the fabricated antenna.

There is discontinuity in the two substrate physical structure 

What is the PC board material .... fiberglass epoxy?  FR4?  If so, the top layer with the microstrip antenna outwards, the inner layer unclad board. They can be bonded together with very thin layer of epoxy 

 I have extensively used this technique to realize thickness of 3.2 mm, it works. You should take two single side copper substrate and join them from open sides (Have you joined two double sided copper substrates?)

If you are having substrates of copper cladding both sides then first remove one side copper and then by the use of some mechanical press sandwich both the substrates having copper on outer sides with some non-conducting adhesive. 

Mention with which substrate you are trying to design your model?

I think the main problem is alignment of the two substrate any shift within 1 mm give you different result.

Why u want to stack two layers of 1.6 mm. In market u will find 3.2 mm thickness material also. Better go for it coz when u make staking u may face problem of air gap which leads to distortion of antenna parameters.

I need to clarify something before I can help you. How are you feeding the antenna? Is it a probe feed, coplanar waveguide feed, or one of the microstrip feeds?

If I understand you correctly you are make the patch on a 1.6 mm board with a ground plane on the back and then manually attach a second two sided 1.6 mm board to it?

One more question. What are you using to model the antenna?

I'm a firm believer of the adage that all models are wrong, some models are useful.