what does it mean when a guy sighs a lot around you?

we had a short "fling" (i broke it off) but we're still friendly towards each other. I've noticed though that whenever he comes over to talk to me he never has much to say yet sticks around as if we're having a real conversation. And he's always the one approaching me never the other way around.

Also EVERY single time he's about to open his mouth to say something he'll let out this big sigh, I don't know if he does that with everyone, but I don't think he did that before we "drifted apart".

i'm just confused bc if its a boredom sigh then why does he continue to stick around and approach me first? and if its not a bored sigh, then why does he dramatically sigh so much?
what does it mean when a guy sighs a lot around you?
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