When to add a waist stay?
Here is what I found after researching a bit more:

A waist stay is typically made out of a sturdy ribbon (grosgrain or petersham), tacked at the natural waist. The stay should be slightly smaller than the garment dimensions.

The purpose of the waist stay is to help carry some of the weight of the garment and lessen the strain on the bodice.

Without the stay, the dress is held up by the bodice. A heavy skirt will tend to pull the dress downwards, which is not good for strapless styles!!

With the stay, the dress is "anchored" at the waist (because this is now the tightest part of the dress). The skirt will be secured to the waist, and a boned bodice will also be held up from that point. This lessens the strain on the bodice and zipper (if applicable).

This can help the garment feel more secure and less likely to fall down. It shouldn't significantly change the fit, but should help for wearing over longer periods of time by making sure the dress stays where it's supposed to and doesn't sag.

Some sources:


http://www.lauramaedesigns.com/2015/08/adding-waist-stay-to-garment-tutorial.html
http://blog.gorgeousfabrics.com/2012/04/05/the-what-and-why-of-waist-stays/
https://www.lovelyandenough.com/blog/2015/09/waist-stays-and-weddings