To me, the harness wiring thinkness / wire gauge that leads to the socket plus the circuit 3A fuse is too light to handle the amps drawn by your compressor. If you simply install a higher amperage fuse, the wiring may over-heat and end up causing a fire if the fuse holds out or even cause the surounding harness insultation to melt thereby causing unwanted problems.
Homesley is correct with his advice to power your compressor directly from the battery.
Perhaps you should connect an aftermarket cigarette lighter female socket to your battery for this purpose. Ensure that the add-on socket is fused and connected to the correct polarity.
When the socket is not in use, it can be tucked under the seat or you can mount the socket in a location of your own choosing, for easier access. If you do mount the socket in a location other than under the seat, make sure that the socket can be protected from weather conditions when not in use.