Romeo does not fight with Tybalt first because he's afraid of Juliet's reaction. Describe how her reaction supported his fear.
I think you've got a bit muddled here. Romeo gives two reasons to Tybalt as to why he won't fight with him (Tybalt, of course, is fighting Romeo because he saw Romeo - who shouldn't have been there - at the Capulet party!):
Tybalt, the reason that I have to love thee
Doth much excuse the appertaining rage
To such a greeting. Villain am I none.
Therefore farewell. I see thou knowest me not.
I do protest I never injur'd thee,
But love thee better than thou canst devise
Till thou shalt know the reason of my love;
And so good Capulet, which name I tender
As dearly as mine own, be satisfied.
Romeo's reason for not fighting Tybalt is that - because he is now married to a Capulet - he should "love" his relation, rather than hate him. He tenders the name Capulet - now that he is married into the family - as dearly as his own name of "Montague", and begs Tybalt to leave the fight aside.
His reason for this is because him, Juliet and Friar Laurence have come up with a plan that - after they are married - they can publish their wedding publicly and heal the family's feud. Obviously, Romeo, who thinks he's about to heal the feud, isn't going to fight Tybalt.
So it isn't because he's afraid of Juliet's reaction. It's because he hopes his marriage will bring an end to the feud between the families. And her reaction - huge upset at Romeo's banishment, and no real anger at him for killing Tybalt - only reiterates how much she loves him.