Be reassuring and supportive. They seem nice, and they've suffered enough already.

"So your sister Olivia has a fairly bad fever. I think I have some aspirin in the medical cabinet she can have once she is awake."
"Right... Thank you."
"Other than that we can probably expect her to be mostly bedridden for a week at least."
"Yeah, it seems that way. Should we call the hospital?"
"That's up to you and her. I think she would be fine as long as she just stays in that bed for a couple of days."
"But... but we can't stay here! You have already been far too kind... and... and..."

The decision to help the sisters has just come so naturally to you that you only just now really realizes how weird of a situation it must be for Vanessa to have a sick sister and has to rely on an absolute stranger for support. Your eagerness to help them might be weirding her out a bit. It can seem a bit like you are taking advantage of their situation. Still, you try and argue your case.

"Listen, Vanessa, let's calm it down a bit." you say trying to stabilize the situation: "If you go out there again, you're putting both yourself and especially Olivia in danger. We can call a hospital, but how would you pay for the care? Do you have insurance? Do you even have a home?"
Vanessa looks down on the ground with a stare as vacant as the floorboards. A grim display of defeat washes over her beautiful face. A silence proclaims its existence loudly. Tears are retreating over her cold red cheeks. Ten long seconds pass.
"You're right." she sniffles. "We cannot pay the hospital bills. We do not have insurance. We do not have a home. It's winter. All of the homeless shelters are more than likely completely full. We don't have anywhere to go."
"Wouldn't it be best to stay here? At least until tomorrow? It's late. It's already half past nine; there is no good reason to go outside. We can talk about it again tomorrow, and hopefully Olivia will be awake by then, and you can talk about it together."
"Yeah." she says meekly.
"Don't worry about being a bother, okay?" you reassure: "I don't know what you two have been through, but it seems to me that it has been rough. If you want anything to eat, or a shower, or to borrow some of my clothes just ask, alright?"
"Thank you." her meekly tone persists.

You spend the evening preparing a pretty simple and quick ready-meal lasagna that can be reheated in a microwave in case Olivia wakes up later. While you're doing that, Vanessa is taking a shower, and afterwards she put on some of your clothes that she has borrowed. She gets out of the bathroom just in time for you to be done with the meal. You serve it on the small dinner table.
You give Vanessa a goofy smile: "Sorry, it's not exactly Michelin Star tier food I have served here. If I knew I would be having guests today, I would have prepared for something a bit more extravagant."
Vanessa just meekly replies: "It's fine. Thank you."
That does deflate the mood a bit. The dinner is mostly silent. You have a hard time reading Vanessa's face. She may be sad, she may be relieved, she may be confused, or she might just be a bit worried. You're not really sure.

Suddenly Vanessa starts to cry again. You are not really sure what to do, but before you can even really think about it, she looks up at you again, feelings of bewilderment and turmoil twirling in her tearful eyes, and she desperately whimper:
"WHY?"
"Wh-" she cuts you off.
"Why are you being so nice to me? Why are you being this impossibly kind? Why can't you just be a shitty shallow person? If you were just being nice for my body or something, I wouldn't be this racked with guilt."
While her mistrust is a bit hurtful, you do kind of see where she is coming from. Also she has had a very rough day, so a bit of irrationality can probably be excused.