Having said that there's no need to avoid all tweed on the grounds that it is a fundamentally frumpy fabric, I would like to suggest that woman of all ages approach it with caution. Certain outfits might seem to look acceptable on younger women, and, as a general rule, I don't consider 'acceptable' anywhere near good enough to warrant adding to my wardrobe. Take Karen Millen's neon tweed dress as an example. It's so obviously designed to only be worn by a youngster with a seriously good body, I wouldn't touch it with a ten foot pole, not even if it is on sale at a reduced price as I write.
By way of a contrast though, Shea of www.curvesandconfidence.com manages to look seriously fab in her knee length tweed pencil skirt. Her outfit isn't the tinniest bit frumpy looking, thus I see no reason to suppose it would cause a women in her 40s, her 50s or even her 60s to look frumpy. (I know a lot of women who might prefer to avoid the kind of heels Shea is wearing, not because they're particularly high or uncomfortable-looking but because the heels are a tad delicate and might wear down a bit too fast to be bothered with on a hugely regular basis.)