The lines "Tybalt, the reason that I have to love thee/ Doth much excuse the appertaining rage/ To such a greeting: villain am I none," suggest that Romeo desires to reconcile with Tybalt and end the feud between the Montagues and Capulets. He recognizes that his love for Juliet, who is a Capulet, is a strong enough reason to overcome any anger or resentment he may have towards Tybalt.
The line "This day's black fate on more days doth depend;/ This but begins thüwoe others must end," suggests that Romeo recognizes the destructive consequences of the ongoing feud and desires for it to end. He recognizes that the events of the day, including the death of Mercutio and Tybalt, are just the beginning of the suffering and tragedy that will result from the ongoing conflict.