Continuing in the Aldridge and Co. catalogue (1859), the "Under-Shirts" section contains selections (presumably of woven cloth) for boys, misses, ladies, and men in a variety of fabrics. There's also "Men's Knit Wool Jackets, in great variety."
The categorization of the catalogue can be somewhat random, and here we have "jackets" in the "under-shirts" section, but we also know that whatever they were, they were available "in great variety."
I do know they had a sort of knitted t-shirt (if you look at your modern t-shirt, you'll see it's knitted too), but maybe the knitted jackets looked something like these sailors on the deck of the U.S.S. Monitor.