What sort of headgear would be appropriate with a black watch tartan?
Unless you're doing some sort of military reenacting, the tartan is irrelevant. Any hat that is appropriate with a kilt will be appropriate with Black Watch.

what sort of modern headgear would be used in summer? in winter?
I'm assuming that when you use the term "modern headgear", you're not asking about traditional Scottish bonnets. In which case, wear whatever you like. There are no rules. I think we've pretty much seen every type of hat worn with kilts, from ballcaps to sombreros.

In cases where I'm wearing the kilt and not necessarily trying to stick with Scottish tradition, I've recently become a convert to Tilley hats for practical headwear. In summer, I like the ventilated "Airflo" Tilley hat. And I recently picked up a Tilley winter hat (made from wool) that I can't wait to wear when the weather turns cool.