In terms of Shakespeare's play, Romeo and Juliet, there are two themes that tie into the concept of "love at first sight."
The first theme is that of fate's part in the meeting of these "two star-crossed lovers." In the prologue, the chorus introduces the plot of the story before the characters even take to the stage:
Two households, both alike in dignity,
In fair Verona, where we lay our scene,
From ancient grudge break to new mutiny,
Where civil blood makes civil hands unclean.
From forth the loins of these two foes
A pair of star-cross'd lovers take their life;
Whose misadventur'd piteous overthrows,
Doth with their death bury their parents' strife.
(Opening Prologue, 1-8)
There is a great deal of information in the prologue to the play. We learn that there is a feud between two noble families. And ironically, out of this hate between the two families, Romeo and Juliet meet and fall in love, but they are already fated to die. And their deaths are the only thing that ends the feud. The Elizabethans believed that each person's fate was determined before he/she was born, and nothing could alter that. Regarding themes, eNotes.com reports:
...Shakespeare amplified...his source's emphasis upon the Elizabethan concept of Fortune or Fate. Upon learning of Mercutio's death, Romeo exclaims,
"This day's black fate on more days doth depend, / This but begins the woe others must end" (III.i.119-120).
In Act III, scene v, Juliet addresses Fortune and implores its aid:
O Fortune, Fortune, all men call thee fickle;
If thou art fickle, what dost thou with him
That is renown'd for faith? Be fickle, Fortune:
For then I hope thou wilt not keep him long,
But send him back.
This information stresses the characters' attention to the presence of Fate or Fortune. Fate, they believed, was the plan the universe had in store for every individual; Fortune refers to one's luck. Fate stands fast, but Fortune is "fickle:" it changes its mind—cannot be controlled or predicted. Romeo notes at Mercutio's death that the fate which brought about this dark deed is only the predecessor to more bad things to come. Juliet personifies Fortune, asking it to be fickle, or changeable, so that Romeo, who has had the misfortune to be banished, will return soon.
Another theme that might affect the statement of "love at first sight" could be love vs. hate. Romeo and Juliet have found love, while their families hate each other. eNotes also refers to this conflict in that:
...the cause of which is never mentioned and cannot be recalled...
If no one remembers why they fight, how can it be important any longer? Referring again to the prologue at the top of this posting, we are told that there is a long-standing feud between two noble families of Verona.
Romeo's paradoxically acknowledges the conflict in his love for Juliet:
"My only love sprung from my only hate!" (I. v.138)
Later, after Romeo has killed Juliet's cousin Tybalt, she first chides him over the other man's death, but forgives him due to the circumstances which led to the fight. She loves Romeo and clings to him, rather than rejecting him for her cousin's actions and subsequent death at Romeo's hand.
This is a play of love and hate, and "Fortune and Fate." In terms of fate, once the couple meets, there is no turning back: their "doom" is sealed. And the only problem that affects their "love at first sight" is not their love, but the hate of their families.