"The Weight" by Tim Maleeny

From: Alfred Hitchcock's Mystery Magazine July/August 2007. Ed. Linda Landrigan.

Police officer Danny Rodriguez stops by for a few beers with his retired partner Sam. starting a story with, "I found a dead pimp last week." He goes on to identify the pimp as Shortball, a midget drug addict whom they both knew. With the mayor cracking down on the department's homicide closure rate, no one is looking very hard into Shortball's apparent suicide, but Danny believes it's suspicious.

As Danny details his independent investigation, we learn that Sam has lost his wife to cancer, been fitted with a prosthetic leg, and is struggling at a relationship with his daughter Sally, who believes his time away from home contributed to her mother's suffering. Danny wraps up his story revealing that he tracked a runaway girl to Shortball and that he believes the girl's father may have killed Shortball and made it look like suicide.

You may have guessed this is a friendly-visit-to-trap-a-suspect story, but Maleeny executes it well.