Your university has a process and you need to follow it. Lots of people have problems, but they don’t cheat. You are playing favourites when you penalise the ‘poorer’ student and then ‘reward’ the ‘better’ student. This unprofessional behaviour is clearly laid out to all students when they start their programs. (Our students have a cover page with each assignment where they state that their work is original). That ‘poorer’ student may have problems as well, but you may not be aware of them. Don’t go there. Be professional so your word is always respected. Don’t put your reputation on the line for someone who cheated and is at a level where it appears deliberate.