# the encouragement that instructs you

"what God has instructed you in the scriptures to encourage you"

# as sons ... My son

The word translated "sons" and "son" is specifically the word for a male child. In that culture the family line continued through the sons, not normally through the daughters. 

# My son ... corrected by him

The author is quoting from Proverbs 3:11 in the Old Testament, which was the words of Solomon to his male children.

# do not think lightly of the Lord's discipline, nor grow weary

"take it very seriously when the Lord disciplines you, and do not grow weary"

# nor grow weary

"and do not become discouraged"

# you are corrected by him

"he corrects you"