What impression of Tony do you get from his comment, "I can bear witness to that"?
You'll have to answer this question for yourself because it is asking for your opinion. I can give you my opinion.
The action of Act III centers around some missing jewels. Constance has asked Mrs. Hardcastle's permission to wear the jewels that are rightfully hers. Mrs. Hardcastle doesn't want to give them up, so Tony tells her to say they're missing, and he will "bear witness" that they are gone. He means, "I'll back you up" or "You're right about that."
The impression that gives me of his character is that he is devious and conniving--not someone I'd readily trust.