How is the formation of limestone caves connected with the geolegical term of weathering?


Its because they are both made by erosion. Limestone is a rock that is soft and easily eroded by underground streams and rivers. Just as water can carve mountains down and cut canyons above ground, they do the same below ground. After this water recedes, The water has cut passageways and tunnels into the rock leaving crevices and caverns. This can be seen in the TAG (Tennessee, Alabama and Georgia) area of caves. There are over 2500 caves in the area where the three states meet. Most are limestone caves made with the above mentioned process. Great place for spelunking as well.

Not quite. Limestone can be quite hard but in any case mechanical erosion is a secondary process consequent upon a sufficiently large conduit forming first.

The primary process is the dissolution of limestone (strictly speaking the calcium carbonate that is its main constituent) by water slightly acidified by absorbing atmospheric carbon dioxide.

The water finds its way through the rock formation by following the tension-cracks, bedding-planes and other discontinuities from sink to rising (spring).

And the term used throughout the English-speaking world is "caving" not "spelunking", which I have heard is actually derisory slang in the US for novice or dilettante cavers. I've mentioned this a few times on Answers by now!