One way in which Romeo does not fall in and out of love easily is that while Romeo is fickle, he actually does remain in love for a long period of time. He is first in love with Rosaline for a long time, and then he is in love with Juliet to stay.
One piece of evidence we have proving that Romeo was in love with Rosaline for a long time is seen in the opening scene. After Benvolio tells us that he saw Romeo at dawn on the west side of the city under a sycamore tree, Romeo's father informs us:
Many a morning hath he there been seen,
With tears augmenting the fresh morning's dew,
Adding to clouds more clouds with his deep sighs. (Act 1, Scene 1)
This passage tells us that Romeo has been acting sorrowfully for a very long time. We may be able to assume that Romeo stands on the side of town where Rosaline lives, pining for her all night long. Since Romeo's father states that Romeo has been seen crying at dawn for a long time, we know that Romeo has been in love with Rosaline for quite some time, therefore, Romeo does not fall in and out of love easily.
However, we also see Romeo as being quite fickle. Even though he has been loving, or lusting, over Rosaline for a long time, it does not take him long to transfer his affections from Rosaline to Juliet. Romeo falls in love with Juliet the instant he sees her, as Romeo declares, "Did my heart love till now? Forswear it, sight! / For I ne're saw true beauty till this night" (Act 1, Scene 5).
Friar Laurence's reaction provides the best evidence of Romeo's fickleness when he scolds Romeo, saying,
Holy Saint Francis! What a change is here!
Is Rosaline, that thou didst love so dear,
So soon forsaken? (Act 2, Scene 3)
Hence, Romeo's character is one that loves devotedly and for a long length of time, but since he is young and still confuses love with lust, he is also one that is fickle and quickly falls in and out of love.
Romeo is a lovelorn character who "falls in love easily," as shown by his initial love for Rosaline. He weeps and complains over her during the beginning of the play, and she doesn't even love him back. Shakespeare wanted to emphasize the silliness of this kind of unrequited love - "Petrarchan Love" - by utilizing cliches in Romeo's words about Rosaline. He uses a lot of silly oxymorons such as:
"O heavy lightness! serious vanity!
Misshapen chaos of well-seeming forms!
Feather of lead, bright smoke, cold fire, sick health!"
To anyone even modestly educated in Elizabethan times, this kind of talk would have seemed as cliche as sitting under a tree picking flower petals, saying, "She loves me... She loves me not... She loves me..." You get the point - kind of pathetic. So in this respect, Romeo is a lovelorn sap.
When he meets Juliet, however, he learns what love really means. You can see this in the balcony scene when Juliet is being quite mature and serious, and Romeo is still rattling off this kind of old, tired poetry. It can be argued that Juliet must "teach" Romeo to love throughout the play. In this respect, she is successful, because if his love for her were not immensely more substantial than his love for Rosaline, he doubtfully would have killed himself for her in the end.