Hermione cares more about Harry than Ron (btw, I normally shouldn't have to mention this, but please don't pretend that it's an anti-Ron/anti-Romione post 'cause that's not my intention. These are just Canon facts 😇).
The evidence? There are quite a few, so feel free to mention anything I might've missed out on.
In Chamber of Secrets, when Hermione's unpetrified, she runs towards Harry.
Harry didn’t know whether the best bit was Hermione running toward him, screaming “You solved it! You solved it!”
Wouldn't it have been better if she'd said "You both solved it?" After all, although it was Harry who realized that it was a Basilisk, Ron had helped too.
We also don't notice any interactions between R/Hr. Okay, maybe it happened and we just didn't get to see it, but I'm only basing it on what's actually mentioned.
I mean, think about it. Ginny had nearly died and Hermione had been petrified herself. Couldn't she have hugged Ron or something?
In Prisoner of Azkaban, H/Hr rush towards Ron after finding him in the Shrieking Shack, and one of them (maybe Harry, maybe Hermione. It's not specified) asks him whether he was okay. However, Hermione doesn't say anything else to Ron until a while later. And she just "shushes" him. Nothing more.
And when he imbalances, it's Harry who catches him.
You know, Lupin seems to be more caring.
In the fourth book, Hermione seems to want Harry to follow her to the kitchen.
"Harry!" she panted, skidding to a halt beside him (the Fat Lady stared down at her, eyebrows raised). "Harry, you've got to come - you've got to come, the most amazing thing's happened - please -"
She seized Harry's arm and started to try to drag him back along the corridor.
Why? She knows that he isn't interested in S.P.EW., and Ron was present there too. But the first thing Hermione does after figuring out the location is to drag Harry off.
In OOTP, Hermione's reaction when she assumes that Harry was made a Prefect is very telling.
The door banged open. Hermione came tearing into the room, her cheeks flushed and her hair flying (Sidenote: It's quite a romantic imagery). There was an envelope in her hand.
'Did you--did you get--?'
She spotted the badge in Harry's hand and let out a shriek.
'I knew it!' she said excitedly, brandishing her letter. 'Me too, Harry, me too!'
And when she finds out that it was actually Ron:
'No,' said Harry quickly, pushing the badge back into Ron's hand. 'It's Ron, not me.'
'Ron's prefect, not me,' Harry said.
'Ron?' said Hermione, her jaw dropping. 'But ... are you sure? I mean--'
She's really surprised and maybe even a little disappointed.
And in the same book, Hermione appears to be more appreciative of Harry's Christmas gift than Ron's.
'Thanks for the book, Harry,' she said happily. 'I've been wanting that New Theory of Numerology for ages! And that perfume's really unusual, Ron.'
