The phrase "happy sigh" refers to a contented or pleased feeling that leads to taking a deep breath and releasing it slowly, often accompanied by a little smile. Full definition
(long happy sigh) Little does he know that when he wakes up I'm going to ask him to move all the furniture out of the Guest Bedroom, so that he can rip down more drywall, and uncover more of those delicious horizontally - planked -LSB-...] (theletteredcottage.net)