A quick and dirty definition for vessel is "container". A scholar would crap all over that, but it'll do for now I think.
But in a great house there are not only vessels G4632 of gold and of silver, but also of wood and of earth; and some to honour, and some to dishonour.
I consider that men are strong vessels, say... iron pots and women are like earthen vessels or clay bowls. A great house has vessels of all sorts and we have no lack of analogs in our own kitchens.
I can drop kick and chuck around all my pots and pans, and for the most part I could still use them. I'd have to really try to ruin them. My coffee mugs are not so sturdy.
I treat my mugs with a degree of understanding. I take special care not to drop them, I certainly don't stack them like a heathen would, because they may chip. Indeed I treat them with honor. My mugs have their own place and I prefer them not to be touching each other if at all possible. Especially if I have a mug that I like the design on it or some such. My pots and pans are precariously stacked in nonsensical physics defying ways because it basically doesn't matter what I do with them.
Women to me are just like that. Not as strong, not as tough, not as emotionally resilient, not as readily able to focus on abstract principles. Not as easy for them to hold to the truth in the face of deception, if the garden incident is to be included. And yet, of no less value to their owner. (remember...
heirs together) God LIKES His coffee mugs. We pots and pans have our place, and they theirs. We work fantastic when He's cooking. Just put us on a red hot stove for an hour and watch us go. We're terrible for drinking out of. A good coffee mug should be smooth, ya?
Moving away from the metaphor, I should understand and have knowledge that my wife is in many different fashions, inferior. And that knowledge should not lead me to mistreat her or look down upon her, because in these things she is as God designed her to be. The end goal for me isn't to continually attempt to equip her and toughen her up to be able to handle the same things I am able to. There may be some of that here and there, but the bible is clear that our roles and responsibilities and expectations are quite different. If my wife ever succeeds in being as good a man as I am, it is a great shame to me for not being much of a man,
In specific application I think I can only mirror what has already been said. I don't expect her to work like a man. It is enough to work like a woman! It is known she can't just logic her way out of an emotional tempest, like I can. Hormones are wack, yo. I can insist on some standards of behavior, but she needs someone to be gentle with her in a way that is never really afforded to me. If I needed someone to just be understanding for a little while while I had a good cry... well I'd be a pretty thin skinned man. For her, that's fairly normal. Part of giving honor to a weaker vessel is respecting structural tolerance. I can't just keep on her to "fix the issue" whatever it is. Generally speaking the issue isn't even the issue and it's some horrid blend of misapprehension and estrogen that is the issue. I give her space that I would never need and infuriatingly long amounts of time to puzzle her way through things on her own that I promise you I've already explained 10 times. This is not unusual, Jesus does it for His men all the time.
I have a couple examples. Ezekiel was ordered to do a bunch of really uncomfortable things, but balked at eating food cooked over human poop, and God allowed him to cook over cow dung instead. A small comfort, but an actual concession nonetheless.
Better for my purposes is when Elijah had fled Jezebel in 1 Kings 19. Elijah does his best to undo his reputation as a great man of faith by just having a breakdown and asking to die. God feeds him by the hand of an angel a couple of times, and reveals Himself a little more to Elijah, but the man is still inconsolable. Therefore God gives him some final tasks and sends him to go anoint his successor. God does not rebuke Elijah at all in this chapter, but takes it easy on him the whole time. There is a point, I believe, where we need to recognize the breaking point of our women (which is probably well under Elijah's) and make sure not to push them that far. God pities us for we are but men. So too should we pity our women, for they are but women.