There seems to be an ongoing competition between the two throughout the novel. Orlick is willing to work like crazy for that which Pip wants nothing to do with. Pip came from just about nothing, just like Orlick, so this angers him all the more.
Biddy seems to be attracted to Pip's character, Pip doesn't really want her, but wants to befriend her. Orlick feels threatened by Pip's presence with this woman and wants her for himself. She doesn't really want Orlick, so nobody's really getting what they want... which relates to the title Great Expectations. It's not Great Accomplishements, or Great Acquisitions.
Pip does grow weary of Orlick's harsh character as well. His anger is more well-founded when Orlick begins to treat Pip's sister terribly.
Dickens first introduces Dolge Orlick in Ch.15 In "Great Expectations." Pip gives us three reasons for the mutual animosity between them:
1. When Pip was a small boy Orlick the bully would scare him saying,
"that the Devil lived in a black corner of the forge, and that he knew the fiend very well: also that it was necessary to make up the fire, once in seven years, with a live boy, and that I might consider myself fuel."
2. Later, when Pip had grown up and was old enough to be apprenticed to Joe, Orlick began to hate Pip because he thought that Pip would replace him and that he would lose his job at the forge:
"When I became Joe's 'prentice, Orlick was perhaps confirmed in some suspicion that I should displace him; howbeit, he liked me still less. Not that he ever said anything, or did anything, openly importing hostility; I only noticed that he always beat his sparks in my direction." [Ch.15].
3. In Ch.17 Biddy tells Pip that Orlick is attracted to her. This angers Pip and he hates Orlick all the more:
"I was very hot indeed upon Old Orlick's daring to admire her; as hot as if it were an outrage on myself."