Why is it that the weight of an object weighing 1N air, weighs more when immersed in water?

There is no "why", because that's not what happens. The truth is

exactly the opposite.

Whatever the weight of a solid object is in air, that weight will appear

to be LESS when the object is immersed in water.

The object is lifted by a force equal to the weight of the fluid it displaces.

It displaces the same amount of air or water, and any amount of water

weighs more than the same amount of air. So the force that lifts the

object in water is greater than the force that lifts it in air, and the object

appears to weigh less in the water.