Phoebe gave him the glasses because she figured the moment of truth had come, if the Baltimore's were not Connie's family, then they could drop the assumption and ask David to look for Connie's real family.
Her assumption turned out to be the right one as Collin Baltimore let out a yelp and jumped from the chair and grabbed the air in an attempt to touch Connie.
"Co-Connie....?" His voice cracked greatly, he tried to hold back his tears but instead they pushed out like a waterfall. "Connie my God, have you been here in the cafe right from the beginning? What didn't you recognize me, why haven't you moved on this whole time?"
His fingers rubbed away tears, behind the wet glasses. Collin couldn't see anymore so he took them off and dried them with the bottom sleeve of his shirt.