I too am a level 3 TA with some HLTA responsibilities (when there is a last minute teacher absence). Whatever lesson I'm in, in a TA role, I am asked to marked the books for the groups I've worked with in class. I don't mind this as this gives me ownership of what I've done with the group. Its nice to be involved in the class this way and the working relationship between the teacher and myself is great. It is a whole school thing that all TA's mark their own groups work.