Does the axle have brakes on it?
If it has brakes, you have to keep in mind that a significantly taller (and heavier) tire will cause the brakes to be less effective than the stock height tire. Tire diameter is a lever arm on the brakes, and weight is an inertial force that also affects the brakes. Taller/heavier tires/wheels are harder to stop.
I would not put considerably bigger/heavier 16" wheels and tires on an axle made for 14" tires. The braking performance will be practically non-existant after the tire/wheel swap.
I would go only slightly larger in tire diameter and width, on either 14" or 15" wheels.