This is one of the many cliche's that sounds poetic when it is recited during church services or on church television programs. However, when one considers where in the scripture this statement comes from it begins to sound a little less Shakespearean.
Even Paul equates blessings with Obedience.
"Now to him that is of power to stablish you according to my gospel, and the preaching of Jesus Christ, according to the revelation of the mystery, which was kept secret since the world began, But now is made manifest, and by the scriptures of the prophets, according to the commandment of the everlasting God, made known to all nations for the obedience of faith: To God only wise, be glory through Jesus Christ for ever. Amen" (Romans 16:25-27).
Those having faith are moved to obedience because they are confident of the blessings that obedience brings. They know that God is a rewarder of them that diligently seek him (Hebrews 11:1-6).
Sometimes God's blessings come after making thru hard times and remaining obedient. Joseph was hated by his brothers and sold into slavery by them. Eventually he was sold to Potiphar, the chief of Pharaoh's bodyguard (Genesis 37:36). Because of his Obedience everything Joseph did, met with success (Genesis 39:1-6). Because of Potiphar's wife Joseph was thrown into prison. In time Pharaoh had a dream and when none of the Kings advisors could interpret the dream Joseph was sent for Joseph explained both dreams one of plenty and one of famine. Joseph even suggested how to survive the famine (Genesis 41:1-36).
Pharaoh realized that God's blessings were upon Joseph, Pharaoh promoted him from prisoner to Governor of all the kingdom; second only to Pharaoh himself (Genesis 41:37-44).
Job also received God's blessings through hard times. Job was a blameless and upright man (Job 1:1-11). After Satan destroyed ALL of Job's material possessions, livestock, servants, and finally Children (Job 1:13-19), Job never turned away from God, even when he was pressured to do so by his wife and friends. He continued speaking the truth about God (Job 42:8). He accepted correction for being anxious to declare himself righteous and forgetting to vindicate God (Job 32:2). He also acknowledged his sins before God (Job 42:1-6). At the end Job was restored to his former status. His life was blessed more towards the end then it was in the beginning. His associates and relatives brought him gifts (Job 42:7-15). Finally when Job's obedience went up the blessings came down insomuch that Job lived to see his grandchildren to 4 Generations (Job 42:16).
The Conclusion of the Matter:: When obedience goes up; blessings come down. And that's the only way!
May the Lord add a blessing to the consideration of His Word... In Jesus name
Extra Scriptures of Reference