How does Oedipus exhibit weakness and nobility in Oedipus Rex?
The two parts of your question seem contradictory in nature. You want lines that show his nobility, but also want examples of how he is weak. I will list the two separately.
His opening words mark his nobility, as he shows sincere desire to help his countrymen:
You can be confident that I will help.
I shall assist you willingly in every way.
I would be a hard-hearted man indeed,
if I did not pity suppliants like these.
He demonstrates justice and equality in his relationship with Jocasta:
OEDIPUS: Whatever she desires, she gets from me.
And in his remorse for the actions that he did not know he was committing, he demonstrates morality:
Against those two I have committed acts
so vile that even if I hanged myself
that would not be sufficient punishment.
Oedipus possesses pride and a desire for power. His relentless pursuit of information is what brings about his own downfall. Had he been able to let go of his need to "know all", he would have remained ignornant to the destructive news, as so many encouraged him to do. Pride would not allow their opinions to be heard.