My vote is for a Barbour type jacket. It is made of waxed cotton and comes in various lengths. It gives you a country-traditional look, not to overthink it, but it is still casual and, depending on which one you buy, maybe even lightweight. The "BEDALE" model has short snap-shut vents ( designed for riding horses) that make it good looking with kilts, but slightly longer ones also work just fine. If you aren't up to spending $400 for a genuine Barbour, you might check out offerings by Oxford Blue, Kakadu, et al., as offered at Sierra Trading Post. At least one forum member wears a Barbour in his avatar. LLBean offers assorted Field Coats and Barn Coats and Hunting Jackets, all of which look great with kilts. I also think a fleece pullover is a good kilt disarming device, if you want to look "normal".

I also agree with Jock Scot- if you will just wear the tweed all of the time, it will become less formal to you.