"And the candle will cry the wick every night" is a metaphor for the endless pain of not being together, as if the candle burned to ashes and the wax tears ran out. Every night, the candle will drain the wick "is also a metaphor, but it does not use wax tears to describe pain, but uses" starting from ashes "to further reflect the painful feelings, which was later used as a dedication poem, but actually was originally used to express acacia.
Mr Wen Yiduo's Red Candle has more connotation and dedication.