Mine also started to beep just all the time, even with all seatbelts firmly connected. So I disabled the beep. The warning light still pops up, but isn't important in the inspection (no fail for it).
I used AlfaOBD for Android to disable it. You'll need to connect to the OBD with a dongle and as far as I remember, it requires the yellow adapter. Then you connect to the dongle through AlfaOBD, and then you browse in the menu. It was somewhere near the bottom of the "Dashboard" menu. Just a clear text like "Disable seatbelt warning tone" (or something like that). Press it and it will make no more sound, ever. Even after changing the car battery.
The actual issue is probably a poor electrical connection somewhere in the seatbelt connector, though I didn't find any obvious things when I checked the wiring before disabling the beeper. All wires were connected, no broken/gashed wires, no burnt fuses, and nothing obviously wrong. I didn't mess around more, as the airbag wires go with it, so there is a danger of setting off the airbags while messing around.