This rare kanji has no clear standalone meaning. Treat its meaning as uncertain.
絸 combines 糸 (thread) with 見 (see). The exact historical development is uncertain, but it likely relates to inspecting silk or thread.
Thread 糸 being examined 見 suggests inspecting silk or cocoon threads, perhaps for quality.
For ケン, imagine a keen-eyed inspector examining silk threads: keen -> ケン, and the inspector sees 見 the thread 糸.