It's actually pretty complicated, based on what I see from a quick internet search. Venice is built on top of an underground aquifer (a cave system filled with water). When industry began draining the water out of the aquifer, the aquifer took up less space and began to subside, causing the land on top of it which Venice is built on to sink. Now that we know this, Venetians are no longer draining the aquifer, so the rate of sinking is slowing down and will eventually stop.

This is a known problem in geological engineering: draining water out of the ground will generally cause the ground to sink and pumping water into the ground will cause it to rise. Earthquakes have happened as a result of this.

This is a very interesting article:
Venice still sinking .

The article says they had thought Venice had stopped sinking, but now they see that Venice is still sinking - plus the problem of sea level rise!

"Venice is slowly tilting slightly to the east, something scientists had never noticed before. Venice's subsidence was recognized as a major issue decades ago, when scientists realized that pumping groundwater from beneath the city, combined with the ground's compaction from centuries of building, was causing the city to settle. But officials put a stop to the groundwater pumping,..."

So the buildings are pushing the ground down, along with other problems. It's an interesting article - You'll probably like reading it. I'm glad I saw Venice already in 1962 when I was a college student.

Great question. The flooding in Venice is due to a large number of reasons. Yes, the scientists have found that the city is sinking roughly 2 millimeters per year, but it’s not because of the weight of the buildings; it has to do with plate tectonics and the fact that the Adriatic plate (that Venice sits on top of) is subducting below the Apennines Mountains causing the city to sink and tilt east!

On top of that, a phenomenon called “aqua alta” or “high water” causes super high water rises in the Adriatic Sea, flooding the Venetian Lagoon and the rest of the region. These flooding peaks are due to phases of the moon, wind strengths, rain levels, and rising sea-levels due to climate change.