The switch wiring is fine, if the hot is serving the fixture first, you can circuit through the fixture and have a single Romeo to the switch, but white should be marked black as that Romeo is just carrying and breaking the hot leg.
What I'm thinking is one of the black white pairs at the light should be hot in and the other pair is to the switch, assuming this switch operates this little light. If so, the white wire of the hot pair needs to attach to attach to the silver screw of the light fixture. The white wire running to the switch needs to be marked black and tie to the gold screw of the fixture. The blacks tie together, sending hot to the switch, the switch breaks the hot, sending power back to the light on the white (marked black) hot carrier wire. Now you'd have a hot and neutral connected to the light as intended.
But you need a voltage meter, preferably one with an ohms tester, to test hot/ neutral coming in and use the ohm meter to test the other wire as a complete circuit broken. Y the switch.
Hopefully that reads in clear English...