The Great Gatsby, any exhibition of complete self sufficiency

I'd like to know if "self sufficiency" in this extract from the first chapter of The Great Gatsby means "self-confidence" or rather "arrogance", "conceit", and if "tribute" means "admiration" or "respect"?

The younger of the two was a stranger to me. She was extended full length at her end of the divan, completely motionless and with her chin raised a little as if she were balancing something on it which was quite likely to fall. If she saw me out of the corner of her eyes she gave no hint of it—indeed I was almost surprised into murmuring an apology for having disturbed her by coming in. (...) At any rate Miss Baker's lips fluttered, she nodded at me almost imperceptibly and then quickly tipped her head back again—the object she was balancing had obviously tottered a little and given her something of a fright. Again a sort of apology arose to my lips. Almost any exhibition of complete self sufficiency draws a stunned tribute from me.

Thank you.