So...kind of off-topic, but I thought of it earlier when I was at work, and couldn't type it out.
Basically, we've only been in Mami's life for two or three weeks, roughly. She's come a very long way in so short a time, yes, but it's worth noting (and remembering) that she undoubtedly still feels like going to bed with someone to cuddle up with is absolutely a novelty (in the sense that it's totally new and remarkable).
Also, while it might seem bizarre and unhealthy for Mami to have developed such strong feelings towards Sabrina (including love) in such a short time, it's worth keeping in mind that we've spent a ton of time with her in the past few weeks, and we've been through a lot together. Mami's been at her lowest point since she contracted, and Sabrina not only stayed (even when Mami told her to go away in a moment of distress), she helped her through it. She's had her trust in Sabrina tested and reaffirmed. Sabrina has been completely understanding and patient with Mami and all of her flaws, issues, and fears, while also singing her praises and reassuring her with regards to her fears.
In that context, developing feelings of love so quickly makes sense, and is not unhealthy by any means. In highly unusual circumstances, intense feelings can be developed in a very short time span because what normally takes years can instead be done in days.
This is similar to how Homura has come to develop such a strong bond with Sabrina. Having someone who fully understands and accepts her and what she's done--and praises her for it, no less--is not something she ever expected, to say the least. Also, she's probably gotten more hugs in the last few weeks than she's gotten in her entire life before then, combined. That leaves an impression.