Surely with you is correct too? You say what is wrong with you not 'on you'
No, because 'arnat ti' comes from 'ar' meaning 'on'.
Not everything can be literally translated in Welsh, and so it is in this instance, in terms of illness. So, 'Mae annwyd arnat ti' literally means 'A cough is on you' but actually means 'You have a cough'.
Here is a good link: http://www.bbc.co.uk/wales/welshathome/textversion/sw_e_bedroom_bed_illness2.shtml
Huh, I wonder if that's the root of old curses like "a pox on you!" or "a plague on both their houses!"
So why mark "thee" wrong? Sure it's old-fashioned but perhaps some of us will hear "Diolch i ti" in Chapel.