So... I married Grelka!
She said it was "the happiest day of my life".
But I have to get her to wear something beside that Leather Armor...
What's the best way to do that again?

Not possible on console I'm afraid.

Followers will equip anything that's better than their stuff, in theory. It might take some messing around, improving at the smithy or enchantments to get them interested... then dismiss the follower and pickpocket their old stuff that you don't want them to have. You may have to pick their pockets a few times to clear it out, should it reset.

The problem with that is that followers will wear anything that has a better AR than what they have on, but clothing has no AR. So to go from armor to clothing is impossible without console commands. (Clothing to armor, on the other hand, is easy.)

Even with console commands, NPCs will often revert back to their default equipment whenever they go through a transition: inside a house to outside, for example--anything that involves a loading screen. If you've taken their default stuff, they revert back to their underwear--maybe not such a hardship for your character, but hell on roleplay!

Anyway, if you want to try using console commands, it's simple: look up (on http://www.uesp.net/wiki/Main_Page or the http://elderscrolls.wikia.com/wiki/The_Elder_Scrolls_Wiki) the Item ID of what you want them to wear, then select them, open the console and type

equipitem

Grelka won't follow (she's my wife).

I used the console command "openactorcontainer 1" on her, and her inventory opens up like any other container or chest.

But her Leather Armor does not display...

And I want to dress her in super expensive (Jarl/Thane) clothing.

I've seen guys quote the console command technique for this (but can't locate those threads).

Yes! sounds familiar...
But I recall there were instructions to prevent the clothing from ever resetting.
I guess I could try removing the Leather Armor with console command (even though I can't see it in her inventory).
But I'm no ~console expert...

Couldn't you just give them something good, steal their old stuff, take back what you gave them, then issue some enchanted clothing that enhances their preferred skills somehow, so it's favored?

I seem to remember messing around with clothed followers early on, I just don't recall the complications if there were any.

Neither am I, and the one time I tried it, I evidently didn't do whatever you need to do to prevent the clothing from resetting. My character had married Senna and I wanted her in normal clothing as opposed to those hooded robes she normally wears. At first she kept reverting back to her default robes; then I unequipped the robes (unequipitem ) and equipped the other clothing and she'd end up in just her underwear.

Might be something iffy happening from using the console commands as well, I honestly have no idea.

No, because NPCs don't take enchantments into consideration when choosing what to wear, just AR. All clothing has no AR, so it's all considered equal. That means if their default outfit is armor, they'll never pick clothing over it, and if their default outfit is clothing, they might (randomly) equip it at times if they're a follower, but you can never predict when or where. I've had that happen with Marcurio choosing different enchanted robes than those he starts out with, but it's purely random (and not very frequent). If they're not a follower, the chances of them voluntarily equipping different clothing than those they start out with are practically nil.

Grelka actually has some cheapo 5-gold clothing in her inventory, heheh...

But I'm gonna strip her naked and keep her locked in the bedroom in Solitude!

No, wait - my daughters are right next door...

For PS3 I've taken the follower's clothes and everything and then given them some armor or clothes. They wouldn't wear it so I just quit trying, but when I left and came back to the game, they were wearing it. I'm not sure if it works every time but it works for some things.