This phrase is casual and often used among friends or acquaintances, not in formal situations. After the poker night, John was into me for fifty bucks.
Pro Tip 2/3
Figurative Debt
It can imply a non-monetary debt, such as owed gratitude or help. Since you helped me move, I'm into you for a favor.
Pro Tip 3/3
Friendship Dynamics
It may reflect trust or closeness, being comfortable owing each other things. She's into me for some advice after all the times she's helped me.