weightlifter (as in one who does Olympic-style weightlifting): αρσιβαρίστας, αθλητής άρσης βαρών.
On a more casual level, (ie.one who trains with weights at the gym), you could use the term "αθλητής βαρών".
weightlifting: άρση βαρών
I do weights: κάνω βάρη
I lift weights: σηκώνω βάρη
weight...