"Grace Greater than Our Sin"

At church this morning, we sang the hymn, "Grace Greater than Our Sin".  According to the hymn, God's grace is greater than our sin.

The author of the hymn probably meant that God's grace is sufficient to forgive any sin that we have committed (well, except for the sin of blasphemy against the Holy Spirit, though the hymn does not mention that), provided that one believes in Christ and accepts Christ's sacrifice on the cross.  But are there other ways to see grace as more powerful than sin?  Could grace be more powerful than sin because God accepts us and favors us, regardless of the depth of our depravity?  Could grace be more powerful than sin in the sense that God's grace can outshine and overcome the darkness that is within us?  Could sin be more powerful than sin in that it can reverse the effects of sin for all of humanity?  I doubt that the author of the hymn herself was a universalist, for she was a Presbyterian, and one line of the hymn says that "Sin and despair, like the sea waves cold, threaten the soul with infinite loss", which seems to imply hell.  But I can sympathize with the universalist sentiment that the effects of God's grace should be greater than (or at least equal to) the effects of human sin.  If sin brought condemnation and moral corruption to all of humanity, why can't grace bring forgiveness and spiritual transformation to all of humanity, even if the effects of grace are not experienced immediately in the life of every single human being?  Is grace more powerful than sin, or not?

And is grace more powerful than sin when it comes to my view of others?  What takes up most of the space in my mind?  Is it bitterness, resentment, and judgmentalism?  Or is it a recognition and acceptance of God's unconditional love for me, and an appreciation of the fact that others are people of value in their own right and make mistakes just like everyone who is in the process of growing up?  I have to admit that, so often, the negative takes up more space in my mind.