Hanging sleeves (sometimes called "long sleeves" in contrast to "wearing sleeves", the actual functional sleeves on a bodice/jacket) were worn across western Europe among the wealthy in the very late 16th and early 17th centuries. The famous Ditchley portrait of Queen Elizabeth I by Marcus Gheeraerts shows probably the most extreme example, with the sleeves reaching all the way to the floor; more reasonably-sized sleeves turn up in a huge number of other portraits attributed to Gheeraerts, such as those of Mary Hungate, Lady Frances Cavendish, and Dorothy, Lady Done, and in portraits painted by other people, such as this one of Margherita Gonzaga, this of Doña Marianna Stampa Parravicina, or this by Cornelis de Vos. And this genre painting by Frans Hals!
The style developed out of the mandelion, a man's jacket with open seams and these decorative hanging sleeves, and was transferred to women's garments. There's really no function other than fashionability and conspicuous consumption - the expensive part of any garment was the cost of the fabric, so adding in another yard or two of satin or velvet was a significant increase in price. As an element of fashion, it doesn't tend to turn up in artworks depicting the lower middle classes or poor. So I wouldn't call it "common" in the sense that these were seen as "just the way we make a gown", but it does seem to have been a relatively consistent design element in the upper classes in the Netherlands as well as England, Spain, Italy, etc.
I'm looking at the picture more closely, and they aren't multiple sleeves -- those are panels of fabric that would hang down from the shoulders behind the arms were the wearer standing. You can see the actual sleeves, distinct from those, if you look.