Why is my desk lamp base so heavy?

Deliberately, so the lamp does not tip. The base has to out-torque a fully extended arm holding the head at its furthest reach, so manufacturers add steel plate or cast zinc inside the housing purely as counterweight.

Why it happens

A sprung arm at full extension puts the head a long way from the base, and the resulting moment has to be resisted by base weight alone. The cheapest dense material that fits inside the housing wins, which is why a plastic-looking base is often a polymer shell wrapped around a steel plate.

A light base is a reliable sign the lamp has a short arm, a limited reach, or a tipping problem you will discover the first time you position it over a keyboard.