A short time or short distance.
"The cat had an accident and left a small puddle of wee on the carpet."
Urine.
In plain English: In this context, wee is not used as a noun but rather as an adjective meaning very small.
"He was in such high spirits at the wee that he could barely keep his feet still."
eliminate urine
"Again, the cat had made on the expensive rug"
To urinate.
"The baby woke up in the night to wee on his diaper."
(used informally) very small
"a wee tot"
Small, little.
"The wee puppy curled up on the rug."
obsolete emphatic of we
"Thou wee!"
The word "wee" comes from Old English words meaning "weight." Originally, it referred to a small amount or little bit.