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