I'll give more context.
<"There's no ducking this one," I(father) said, pacing back and forth in my empty living room, the sun speckling the porch outside. "There are no shortcuts." (to his son who might be smoking) I sounded pompous and utterly unconvincing. But when I put the phone down, I felt calmer; tweedish as I'd come across, at least I'd said it.>
I think he means "stuffy". Note the reference to "pompous". That's my interpretation, at least.
(Thank you for providing context. Just as a reminder, quoted references should give the source and be limited to a maximum of four sentences, which you've succeeding in doing very nicely here. We are missing the source of the quote.)