Is there a physiological reason or effect to a 'Heavy Sigh'?

My dog was abused before I got him. I’ll coax him into bed and he’s all stiff and fearful. I’ll give him snuggles and scritches and eventually, he’ll let out a Heavy Sigh and settle in. What’s going on here?

An obvious speculation: A tense critter would tend to hold its breath and not breathe freely. When he relaxes, then he stops doing that and takes a deep breath.