Mirá, flaco, la verdad que no te banco y me voy a ir, porque no te soporto.
Look, dude, the truth is I can't stand you and I'm going to leave, because I can't put up with you.
[Caption 41, Muñeca Brava > La Apuesta > 4]
The verbs bancar and soportar both have pretty much the same meaning as aguantar: "to tolerate," "to put up with," "to stand" etc. For emphasis, Mili is employing each verb, negated, in separate phrases "no te banco" and "no te soporto" -- she does not want to hang out with Ivo!
Bancar is the less formal, and you will probably only find it employed this way in "Southern Cone" countries, such as Argentina and Uruguay.
¡Estoy harta de Juan! No lo banco más.
I´m sick of Juan! I can´t stand him anymore.