Everyone would assume Tim is the stalker of the family. After all, he did spend most of his childhood following Dick and Jason during their times as Robin and even went as far as to become a Robin himself. What most don't assume is that everyone else in the family is stalkerish in their own right. Especially not Steph.
Yes, Steph is an oddball, but in this family? It's not surprising. Everyone has their own quirky thing whether they'd like to admit it or not. Even Bruce has his little quirks that he doesn't really notice and no one bothers pointing out. It's just... Steph's quirky nature is a little too quirky.
In her eyes, it's not a big deal. She tells herself she's just helping those who need it and protecting them. By breaking into their homes and stalking them through the Gotham streets. It's nice to have someone watching your back, but when you don't know it's happening? That's another ballpark.
There's been a new vigilante introduced to the Bats. Obviously, new to the Bats doesn't mean they're new to being a vigilante. They've been around for a while in their own place, but they've recently had one thing or another come up and now they're calling Gotham their home.
Steph, being the protective girl she is, wanted to make sure they weren't trying to pull a quick one over the family. It'd be hard to do considering everyone in the family is a trained vigilante who's been doing it since their teens (or younger). They've all been drilled into being perceptive, for obvious reasons. If they weren't paying attention they probably wouldn't be here today.
Back to the story though. Steph has been following them. Bruce hasn't told her to, but she knows everyone else has been following in their own right, so what's one more to the party? She learned of their civilian identity (asked Bruce and after he told her no she just checked the files on the computer) and figured out their home address, and presumably their base of operations.
It wouldn't be weird if she just kept an eye on it right? Sure it's been a few weeks now, but just to be safe. A precaution, if you will. She's incorporated their address into her patrols so she can check up on their place and make sure no evil-doing is being done. Maybe she's gotten a little too close, but who cares? It's for the safety of her beloved (older) brothers and sisters.
She started teaming up with them for a few missions, and she hates to admit it but she likes them. They're nice to her and she thinks they have an interesting personality. But still! She has to remind herself that she's just doing this to protect the other Bats. No, she's not getting too close to them, what are you talking about.
Fast forward a few more weeks, and she's taken it upon herself to break into their home. Nothing is wrong on the outside, and she enjoys spending time with them, but what if they're different on the inside? She needs to know.
What started out as simple watching turned into going in deeper. Leaving little hints of her. Some would think it's weird, but they don't understand! It's for the greater good! At least, that's what she tells herself as she goes in to hunt more. They haven't noticed anything missing yet, but she hasn't taken anything big. If anything, she's been leaving more than taking.
Almost 4 months have gone by. She's gone from watching to entering. She's forced her way into their life and their home. She's even made contact outside of the masks multiple times. Her family has caught on, but no one's said anything out of worry for the vigilante. She's started to leave bigger gifts. Stuff that wouldn't just magically appear like chocolates or a teddy bear.
Her most recent escapade is taking pictures of the most mundane things. She was in the middle of photographing some trash when she heard a window-rattling. They're home early tonight. Crap. She scrambles to hide her evidence but doesn't have enough time to hide herself before the light is turned on and she's face to face with the danger "Uh, fancy seeing you here. In your own home." Please let her leave.