What is the likely definition of a women's "'health' west" from 1891?

It's almost sure to be a misspelling of vest. In the nineteenth century, at least in London, /v/ and /w/ were either interchangeable, or they were replaced by a sound in between. Witness Sam Weller.

Oxford English Dictionary, under "vest" does list the spelling "west" from the 17th century as dialect. From 1712:

Payd for mackin a west and briches for gouddins child, [£]0. 1. 6.

While west might be an alternative spelling for vest, it might also be a local or regional term for weskit or waistcoat (which at the time was typically pronounced "weskit"), formed as a sort of contraction of weskit, or a blending of vest and weskit.

On the "Health" part of the name:

In this era there was a theory that sweating was good for the health. Ballplayers used to train in wool uniforms to get in some sweating. This might be the reason for the 'health', as a wool vest would be considerably warmer than lighter fabrics.

It could also just be warmer to avoid colds and chills.