Do you find occasionally, just occasionally, you get a headache on a Tuesday? Must be something about Tuesdays...

Normal variation in pressure at sea-level due to weather, eyes of hurricanes and tornadoes excepted, is roughly from 980 to 1035 mbars, a maximum difference of 5.5%. That's about the same as the change from climbing (or descending) 500m in altitude. I'm unwilling to believe the difference is large enough to promote any medical condition. Having been at high altitude in the Andes for over two months, I descended from 3700m to sea-level in a day (by bicycle), thus experiencing a sudden increase in pressure of over 50% in just a few hours, and I didn't have a headache at the bottom. I would have had a headache if I had done it in reverse so fast, and that would have been due to oxygen deprivation.

What seems more likely is that there is another aspect of the weather that is causing the symptoms. High pressure is generally associated with dry weather, and in winter the humidity would be especially low in cold, dry weather. Dehydration is a known cause of headaches.