There's more than one force at play here. There is N UP from the force of gravity pushing you down, and there is N opposite to the direction you are travelling from the force of your motorcycle moving. Therefore, the total N is always more than the weight of the bike and rider. μ is increased by using both brakes, increasing brake-wheel friction which increases tire-road friction which increases μ.
Friction (u) is a constant value, dependent on materials. It doesn't change due to braking. The normal force (N) is what changes. The total force is defined as N x u.
I agree that N is higher than just the static weight of the rider and bike, due to the momentum of the bike.