This one by Jesse Winchester? Various searches have it listed as both "Lay Down" and "Burden of your Heart" and all sorts of other permutations of the two. Hope this helps,
~J

It's a cold cold world
That we're walkin' through
Lay down the burden of your heart.
But it's warm as toast
Walkin' two by two
Lay down the burden of your heart.

Chorus:
Lay down the burden of your heart.
I know you'll never miss it.
Show your Daddy where it hurts,
And let your Daddy kiss it.

It's a fine fine line
Betwixt love and hate.
why it's tough to tell the two apart.
But you know it's love
That He offers you
Lay down the burden of your heart.

Repeat Chorus Twice