with can mean `because of or as a result of `

with can mean `because of or as a result of ` 

ADJECTIVE + WITH + NOUN

OR 

VERB + WITH + NOUN 

Ex. 

They were crying with pride when they heard that their daughter had won the competition.

Our fingers were numb with cold. We could barely feel them. 

He seethed with rage as his boss lectured him.