...but Darcy never shows Elizabeth that he is really glad to see her, does he? Think of Bingley's behaviour very early in his relationship with Jane, when she comes downstairs for the first time after being sick at Netherfield:

[Darcy] addressed himself directly to Miss Bennet, with a polite congratulation; Mr. Hurst also made her a slight bow, and said he was 'very glad'; but diffuseness and warmth remained for Bingley's salutation. He was full of joy and attention. The first half-hour was spent in piling up the fire, lest she should suffer from the change of room; and she removed at his desire to the other side of the fireplace, that she might be farther from the door. He then sat down by her, and talked scarcely to any one else.