When does a sigh hurt?
Perhaps if you have a broken rib, that release of breath could press on your injury and hurt you.
Or if your throat is sore and the air moving past feels like blades running into your tonsils.
Most of the time, though, a sigh is a release of hurt. It may open the floodgates of tears. It may crack open a heart. It may reveal a truth and that truth might hurt, I suppose.
And a spendthrift sigh? A wasted sigh? Why might a sigh be wasted? The sighs of an unrequited lover – are they wasted?
I think most sighs are for the good.