You might want to do some troubleshooting of the brake light circuit. First I'd remove the brake light bulb and try again. Does the headlight still dim or not?
I think you might have a short to ground in the brake light circuit. I've seen this before in "big" motorcycles. Whether removing the brake light bulb changes anything or doesn't should tell you what part of the circuit to look at most closely.
If in fact the wattage of the brake light bulb is higher than spec, that could cause the problem as well.