I hope she runs out of soul trap enchantment soon.
Dropping filled soul gems does not empty them.
Go drunk Miraak, you're home.
If I remember once reading correctly, dropping soul gems only empties them if the soul does not match the gem, like a Grand Gem being filled with a Common Soul and so on. It's always worked for me. I've never tried dropping filled gems that were filled with it's fitting soul, though.
Dropping a Lesser Soul Gem filled with a Petty Soul should empty the Gem. When a Gem is filled with an appropriate Soul it stays filled.
This is how a Gift of Molag Bal works
EDIT Glitch in Your Saved Game, maybe?
Take away Lydia's ability to soul trap.
Problem solved.
Yeah, they're a bit rare, but this still doesn't fix your problem.
I would give her something else until you find another sword.
I mean, having common and greater soul gems filled with petty is one thing, but you're losing grand soul gems, right?
Not worth it. Give her a stick, but save those gems.
Why don't you let her keep the sword, but take the gems off her instead?
You can give her something else heavy to carry instead