Does the weight of a car increase under cornering? Lets say we have a car with a mass of 1000kg, and lets say the car turns a corner fast and pulls around lateral 3g. Since under normal condition car weights 1000 x 9.81 (1g) = 98100 Newtons , will the car now weight 1000 x 9.81 x 3 (3g) = 294300 Newtons while pulling 3g during cornering?
 A: If you're on a flat road and you define the direction of the weight to be vertically downwards(parallel to $\vec{g}:gravity) $; then no, the weight will not change, it'll be $mg$ throughout. If you turn fast enough on the flat road and define the direction of the weight to be radially outwards then it may become more than $mg$ (centrigual force), but most likely the car will topple before reaching that point as friction may not be able to counter the centrifugal force.
Chances are better on a banked road.
If you're on a banked road and driving fast enough, and you define the direction of the weight to be $\perp$ the road, then a component of centrifugal force may make the weight more than the normal weight.(you may define the direction of the weight to be radially outwards too, it can work. Which one of these directions works more easily will depend on angle of banking, coefficient of friction, radius of the turn etc.). The car may topple but not as easily as it would've on a flat road. If even at a banked road you define the direction of the weight to be vertically downwards, the weight will not change, it'll stay $mg$.
