Sydney Carton resents Charles Darnay because in Charles he sees what he could have been. Since the two men look so similar, Carton compares himself to Darnay. He says to Darnay:
“I begin to think we are not much alike in any particular, you and I.”
The main reason that Carton is jealous is Lucie. He falls in love with her from the first time he sees her, and he knows that she is falling for Darnay. He realizes that he could never have a woman like Lucie, but if he were more like Darnay he could. Since Stryver takes all the credit for the legal maneuver that gets Darnay acquitted, everyone pretty much ignores Carton.
“Nobody had made any acknowledgment of Mr. Carton’s part in the day’s proceedings; nobody had known of it.”
Carton is drunk and dishelved (“who smelt of port wine, and did not appear to be quite sober”) and no one considers him worthy of attention, especially Lucie. Carton is usually content for this to be the case, but it is this encounter with Darnay that first gets him to consider the life he might have had.
After Charles Darnay is acquitted at his trial for treason, Sidney Carton notices the way that Lucie Manette looks at Mr. Darnay, and he envies the man.
At the end of the trial of Charles Darnay, congratulations go around; however, no one acknowledges the crucial role that Mr. Carton has played in the acquittal. Instead, Mr. Stryver basks in the victory that has been achieved. Soon, Mr. Lorry hurries off after the Manettes have left. Since the friends of the acquitted prisoner have departed in the belief that Darnay will be kept overnight, Darnay finds himself alone, so Mr. Carton offers to take him to a tavern where they can dine.
After Mr. Darnay eats his dinner, Carton suggests that Darnay give a toast. Darnay asks, "What toast?" Carton tells him, "Why, it's on the tip of your tongue...." So, Darnay says, "Miss Manette, then!" Sydney Carton teases him more about Miss Manette, but Darnay calls for his bill and departs. After his departure, Carton takes a candle and moves to a mirror where he looks at his reflection rather scornfully.
"Do you particularly like the man?" he muttered at this own image; "why should you particularly like a man who resembles you? There is nothing in you to like.... Change places with him and would you have been looked at by those blue eyes as he was, and commiserated...as he was? Come on.... You hate the fellow."
Sydney Carton says that he hates Darnay because the man reminds himself of what he could have become: namely, an excellent lawyer and a husband. Truly, he envies Darnay's character because he has been too weak to become what he should have been.