Isabella is Edgar Linton's pampered and privileged sister whose upbringing stands in sharp contrast to Catherine's. When we first see her, she is fighting over a puppy with Edgar, and she never really grows beyond this adolescent stage. She seems to suffer from a combination of boredom (not a lot to do in Gimmerton) and envy of Catherine.
Her infatuation with Heathcliff comes across as both risky and silly (messing with Catherine's man?). When she marries Heathcliff, she pays dearly by being disowned by Edgar and imprisoned at the Heights by her violent husband. Though we never know for sure, she seems interested in Heathcliff partly because he's a dark and brooding hunk, and partly as a way of competing with Catherine. Then again, there are not many other options for her, unless you count Joseph and Dr. Kenneth.
That she utterly fails to recognize the degree to which Heathcliff is using her (he outright hates her, in fact), speaks to her love of melodrama. Like a fool, she yearns to be with Heathcliff and confesses to Catherine, "I love him more than ever you loved Edgar, and he might love me, if you would let him!" (10.79). For his part, Heathcliff tells Catherine:
And I like her too ill to attempt it [...] except in a very ghoulish fashion. You'd hear of odd things if I lived alone with that mawkish, waxen face: the most ordinary would be painting on its white the colours of the rainbow, and turning the blue eyes black, every day or two: they detestably resemble Linton's. (10.121)
Isabella finally wises up and leaves for London, but not before getting pregnant with Linton Heathcliff, who winds up with both of his parents' worst qualities.