A person who has suffered a cold says:
Теперь я решил побольше заниматься спортом, чтобы закалиться. Всё же закалёниые люди не так подвержены простуде.
The meaning for "Всё же" one can hope here is: "And this because strong people is less exposed to colds". However the translation for "Всё же" in my dictionary is is (con todo, a pesar de todo) "in spite of, despite", "still, however". I think it must be something close to "ведь", something like "and so because...", a continuative conjuntion. Can you throw some light on it? Thanks.