The character who is doing the sitting in this quote is Behrman, an old, cantankerous man, who has come to visit the sick Johnsy. Sue and Behrman came upstairs and "they peered out the window fearfully at the ivy vine", worried that it had fallen. Johnsy said she would hold on to life as long as that last leaf stood there. So, there are a couple possible meanings to the description of how Behrman sits down.
1. He is being very, very careful, possibly afraid that any rough movement will dislodge the leaf on the vine, and describing a solitary miner carefully perching on a kettle (miners had scant furniture) works well.
2. It could just be another literary characterization of Behrman, bringing to mind old, tough, and probably socially awkward miners. His gruff presence is a striking contrast to the artsy, feminine Sue and Johnsy. Henry had already spent some time characterizing Behrman, describing his scruffy beard, and his personality as "a fierce little old man, who scoffed terribly at softness in any one" The miner image fits this well; and it's ironic that is is him at the end that sacrifices himself to save Johnsy.