How do publishers decide whether a book is hard cover or paper back?
It varies depending on the publisher.
Some publishers only publish hard cover.
Some only publish paperback.
For publishers who do both, it depends on the type of book, how many copies they think they'll sell, and how they think the end reader will use it (ex: read it once then give it away vs keep it and read it multiple times). Each publisher will have their own internal guidelines that they use to make this decision.
Covenant and Cedar Fort release all their fiction as trade paperback (trade = the 6x9 size). Shadow Mountain puts their fiction out in hardcover and often sells the paperback rights to other publishers. Deseret Book does a mix of both—The Undaunted got hard cover; Lemon Tart got trade paperback.