Is there any correlation between barometric pressure and the onset of vertigo attacks?

No. The vestibular apparatus, the nerves in the middle ear, do not change their function with changes in atmospheric pressure. However when rapid changes in pressure happen like going up in an elevator in a skyscraper or during landing in an airplane the air space in the middle ear may not readily equalize with the pressure acting on the outside of the body and cause some people to feel dizzy.
Yes. Barometric pressure can directly affect the pressure in the middle ear which can then trigger vertigo attacks.