Jaggers is Pip’s legal guardian and lawyer. He does not really like Drummle so much as appreciate him. He knows what kind of person Drummle is, and that intrigues him. Drummle is strong, and Jaggers appreciates physical strength.
Drummle is an “old-looking young man of a heavy order of architecture” and Pip describes him as a “sulky kind of fellow” (ch 23, p. 130-1). Drummle comes from a rich family. There is absolutely nothing redeeming about his personality.
Heavy in figure, movement, and comprehension—in the sluggish complexion of his face, and in the large awkward tongue that seemed to loll about in his mouth as he himself lolled about in a room—he was idle, proud, niggardly, reserved, and suspicious. (ch 25, p. 139)
Jaggers, remember, lives in a world of criminals. He is familiar with the darkest side of human nature, and seems to feed on it. In fact, since Drummle is such a dolt Pip cannot figure out what Jaggers’s interest is in him. Jaggers refers to Drummle as a “spider” and describes him as “blotchy, sprawly, sulky” but says he likes “the look of that fellow” (ch 26, p. 145)
Through all his stages, Mr. Jaggers followed him with the same strange interest. He actually seemed to serve as a zest to Mr. Jaggers's wine. (ch 26, p. 146)
Jaggers knows that Drummle is up to know good. He advises Pip.
“Hah! He is a promising fellow—in his way—but he may not have it all his own way. The stronger will win in the end, but the stronger has to be found out first. If he should turn to, and beat her—” (ch 48, p. 263).
As usual, Jaggers seeks not to get involve to help Pip or Estella. He seems perfectly happy to let nature take its course. He is not a lover of humans, he is an observer of human nature. He is just happy to have someone to take an interest in, because he knows watching Drummle will be interesting.