The other day saw the last wearing of my lightweight jackets for this season. With exceptions for cloths like linen and fresco that wear cooler than their weights, I organize my wardrobe into warm (8-9 ounce/240-270 gram), shoulder season (10-12 ounce/300-360 gram and cold weather weights (13 ounces/390 grams and heavier) (your seasons may differ and so then should your cloth weights). With temperatures fallen by 25 degrees (F) from their summer highs, it is time for shoulder season cloth.
Shoulder season to my mind is the time for worsteds. The aforementioned linen and fresco work well for summer, and tweed and flannel are all any man needs in cold weather. Worsted wool is relatively tightly woven, smooth, and clear finished, all of which mean it wears warm compared to true summer cloth, does not trap heat as well as woolen flannel and tweed and tends to be both harder wearing and more wrinkle resistant. Which is to say that it fits exactly in the middle.
If winter is the time for double breasteds, which wear a touch warmer due to the overlap of cloth across the chest, and summer the season for single breasted jackets, then either of them works in shoulder season. Best of all is probably the vested single breasted, where the vest helps keep a man warm on cooler days and is not worn at all at the other end of the temperature spectrum (and a reason why that latter configuration is also arguably best for the first half dozen suits in a wardrobe).
That said, shoulder season suits do not have to be ordinary twills. Several of what used to be considered summer suitings - gabardine, solaro and dupioni for example - are among my favorites. And I look forward to wearing them.