The full form of TW is trigger warning.
The acronym “TW” is used to represent the phrase “trigger warning.” A “trigger warning” is defined as an internet label that is assigned to pictures or videos that warns users about the contents before being viewed. Normally, this warning is put on any types of files as a disclaimer that the content should not be viewed by people who are easily influenced to harm themselves in any way.

Origin of TW
There is no origin information available regarding the acronym “TW.”

Example Conversations
A text conversation between two friends.

Friend 1: Did you watch the video that Frank sent to all of us last night?
Friend 2: No, not yet. I was sleeping and didn’t get it until this morning. I didn’t have time to watch it this morning because I woke up late and had to rush to get ready for school. I figured with the TW on it that it is something I better save to watch until after school.
Friend 1: I don’t think you should watch it at all. Honestly, it was in poor taste for Frank to even send it to anyone, but especially to you when you are still dealing with the death of your father. Just don’t watch it.