As marcellus said, it could be that she's hungry, but then, it could be something else. If she's refusing a bf, she's not that hungry. She could just like the exploration and stimulation she's getting from handling her food and feeding herself. She won't be getting much nutritionally from her food, but the experience is obviously something she's enjoying! And if you're eating, she probably just wants to join in. No harm in giving her a little bit of what you're having to keep her happy.

Sounds like you're doing just fine with BLS and there's no issue with offering her something to chew on if she wants it. I wouldn't bother with purees, at her age you don't want to replace her bfs or you might affect the nutrients she's getting. Her weight won't have much to do with whether she needs more solids or not, it sounds like she just wants to set the food agenda. Good for her!