All the above is true and good advice. The key is not the brightness of the bulb, but the power rating (wattage) which will tell you how much current (amps) the circuit will draw. The wiring, switch, relays, fuse, etc. are all rated By how many amps they can pass without damage.
Watts=Volts X Amps
So a 65 watt bulb will draw
65 / 12 = 5.4amps
Assuming 2 headlights, that is 10.8 amps for the circuit.
The next question is how many watts are your brighter bulbs rated for? Do the math. If the new bulbs draw less current than the OEM fuse in the circuit, then you should be ok. It is best to leave a safety factor in there and only load the circuit to 80% (roughly) of the fuse size.
When considering the wire size, the length of the wire in the circuit must be considered because wire has resistance and will reduce the voltage seen at the load (light bulb) thereby reducing the brightness. That is one reason why high current loads are best when wired through a relay. The relay can be close to the battery and the load, keeping the wires shorter for better performance. This also allows you to use smaller wire for the switch that controls the relay and greatly reduces the current flowing through the switch.