What type of chemical weathering causes caverns to form?

For caves in limestone (the most common):

Rain-water & snow melt water absorbs atmospheric CO2, making carbonic acid.

Though weak, this will, over time, dissolve the calcium carbonate that is the primary constituent of limestone.

The water's acidity is enhanced by humic acids from soil cover but it is not necessary for limestone dissolution, and the carbonic acid is still the main solvent.