Okay - Were you using the tilt trim when you blew the fuses previously? If so, try unplugging the tilt trim motor and see if it blows again. Remove the cover and trace the wire from the tilt/trim motor into the lower cowling. There will be a two-prong plug that you can likely access without removing the lower cowling. Unplug it there. If that fixes the problem, you have a sort in the tilt/trim motor plug or harness, the tilt/trim motor has failed internally, or you've lost the ground to the tilt trim motor. If I recall correctly, there should be a ground wire coming off the motor (or near the motor) to the engine frame.
Does the fuse blow with just the key turned on, but engine not running? If not, but then blows when you activate the tilt trim, then you have a dead short in the tilt/trim switch or the wire from the engine to the tilt trim switch.
I'm traveling, so don't have my shop manual. But that # 3 fuse also feeds all your gauges and tilt/trim switch on your control panel. Maybe Mike (HondaDude) will pick up on this thread and tell you the other connections you should check.
Several previous posts with similar problems found that corrosion in the wiring harness was the problem. This typically happens where the harness exits the engine and enters the transom. You may want to peel off the harness cover there and inspect wires for burning, corrosion, and/or chaffing.