Question

why does the viscosity of water increase when sugar is added

Answer 1

Let's talk about "viscosity" first.

VISCOSITY is the resistance to flow.
The THICKER something is, the MORE viscous it is.

For example,
pancake syrup is MORE VISCOUS than oil,
because the syrup is THICKER.
It RESISTS flow.

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Now let's go to our question:
Why does viscosity of water increase, when we add sugar to it?

Well, if the water is warm enough to melt the sugar,
then the sugar mixes with the water, and makes it thicker.
Hence, it's more viscous.

Does that make sense?

(When we melt enough sugar into water, we create something called "simple syrup."
It's just a little cooking/bartending fact.)