How can a Muslim balance good character and overlooking certain rights with strength of personality and demanding rights, taking into consideration situations that some might interpret as weakness, such as dealing with a brother who does not accept advice after being shown kindness, or dealing with someone who procrastinates in repaying a debt?

Your actions of suppressing anger, responding to evil with good, and showing kindness to others are among the descriptions of God's righteous servants. This is not a weakness of character; rather, weakness of character is when a person is affected by evil. Forbearance does not contradict demanding rights and dignity in an appropriate manner. There is no harm in hinting at withholding from someone who reciprocates kindness with ill-treatment, while encouraging adherence to the high status of the righteous.