Tween is a term originally coined by J. R. R. Tolkien (1892-1973) in The Fellowship of the Ring for a hobbit between the ages of 20 and 32. Just as teen is the term for a period of human adolescence (or tens), tween is a further period of hobbit adolescence (or twenties) because of their longer life span. Threen could be used to refer to a hobbit in their thirties, but this was less common. Hobbits weren't considered adult until age 33.
This information is unsupported by the Oxford English Dictionary, which points to an origin in the New York Herald Tribune on August 10, 1941. In addition, Tolkien is not cited, and none of the cites are from the UK.
It's possible Tolkien used the word, but the word in its current use was derived independently.