Abbreviation “TY” means “thank you!” The reason why someone might say this is to simply save time and show you appreciation and gratitude for whatever was done or said
Intention: In this text, someone is using the abbreviation twice to show great amounts of appreciation to you.
“OK, TY for letting me know.”
Emotion: Appreciative
Intention: Someone could be using “TY” in the middle of a text message as a way of saying “thank you.” They could use it as a way of simply saying “I’ve got your message, thank you!”