You need to look at this in a larger context:
It was the first time I could remember they were depending on Leonie to look after me. After Michael left with Big Joseph, it felt weird to sit across the table from Leonie and make a fried potato sandwich while she stared off into space and crossed her legs and kicked her feet, let cigarette smoke seep out of her lips and wreathe her head like a veil, even though Mam and Pop hated when she smoked in the house. To be alone with her.
The marked infinitive you ask about, "to be", parallels the previous marked infinitive "to sit" and in effect is conjoined with it as a complement of weird:
It felt weird to sit ... to be alone with her.