Uzi now can't sleep alone if N, V, or Thad find her before she wakes up.
For N and V, it started a bit after she became their Squad Leader (and V stopped challenging her for the position) where if she ended up falling asleep anywhere but her room, one of them would curl up beside her. For a while usually N, and only VERY rarely V after episode 4, but becoming evenly split for them both later on and especially post series where in general they'd go looking for her. For them it started as an instinctual thing— after all Uzi wasn't asleep high out of the way and reach of anyone who might be (stupid enough to) walk by her, she was in danger so casually! And she didn't even seem aware of how vulnerable she was!!!
For N early on it was also in part to her being his first real friend he could remember having, he wanted to just be around her as often as he could. He tried to curb it when he realized he had a crush on her, but Uzi had thought he was mad at her when she'd realized she didn't really mind it and noticed he was pulling away, he reassured her he wasn't mad at all!! And he ended up doing it again, though really nervous about it. Once SHE realized she had a crush on him, she was mortified, but didn't tell him to stop because she didn't know how without sounding like he'd done something wrong, especially after she told him it was fine.
When V started, it was only after she had awoken from a nightmare after the final battle, of Uzi being put into their same situation by Alice, watching yet another person she cares about being tortured. And, well, she curled right up next to her. Uzi hadn't even shifted because she was used to N doing this by now, and when Uzi woke up later, she was almost too shocked to move, and they didn't talk about it for a while even when V would continue to seek her out.
For Thad he just kinda noticed N and V doing it first and went "oh cool :)" and started doing it too lmaoo.