"Dead Weight" could also refer to Hollister's beloved pistol. He loved it and cherished it so much that he couldn't part with it when he OBVIOUSLY should have - after committing murder with it! So that pistol became like an albatross around his shoulders, bringing him down, or weighing him down. That pistol was a real "dead weight" around his shoulders. That's my take on it.

Now then, as to "Columbo Likes The Night Life"... As is evidenced on screen during the episode, Columbo likes the night life because it's at night when his wife makes lasagna for him. I think the "L" in "Life" was a typo. It was supposed to be "Columbo Likes The Night Wife". That's my take on it.