Pastor Davey Blackburn's sermon "The Weight Of Our Words" focuses on the impact of our words on freedom and relationships, highlighting forgiveness versus freedom. Using the analogy of a dog on a leash, he explains how believers can be held back by old habits despite being set free by Christ. The message underscores the power of words to reflect our inner selves and influence our freedom journey. Ultimately, believers are encouraged to speak words of grace and trust in God's authority for healing and freedom.