They won't let you fly with the duty free liquor that you bought in Belize in the cabin in the US. You can't pack it in your carry-on only into your checked luggage.

Sometimes when I fly via the US I am still required to collect my luggage, clear customs and then there is a drop point nearby to give the luggage back to the airline.

I think when I last went to the UK that the luggage did go straight through which means I would not have been able to continue my trip with my duty free bought in Belize.

What you might want to do is buy your duty free while you are passing through the US. Then they will let you fly with it.

Hey I didn't make the rules, I just try to follow them.

I suppose the deal is that you can purchase and fly with your duty free in the cabin when you purchase the duty free at the port you leave immediately before arriving home. You cannot pass through US TSA check points with liquid. So if you buy the duty free at the US airport within the secure areas you are allowed to carry it onto the plane.