Borderlands 2 is silly but also darker than the first one. Most things are, upon a moment’s reflection, at least creepy and sometimes horrifying. There is lots of comedic sociopathy and black comedy that usually works best when it crosses the line twice. You may be distressed if you pause halfway or reach one of the moments when the game looks back.
For example, Tiny Tina wants to have a tea party. It involves luring a psycho into a trap and torturing him to death … while having a tea party with some dolls. The psychos are goofy insane, and we have a little girl who talks like the internet going over the top, so it’s funny. Did you notice the little name cards at the table, indicating that this psycho got her parents killed? How about that sidequest later on where you get recordings of their deaths when they were captured as test subjects for medical experiments? Or the other recordings from that quest?
On the creepy side, there are Moxxi posters in one (?) of the bandit bathrooms.
The tone is usually pretty light, and the game rarely dwells on these moments. Keep it moving, before the players dwell upon what happened there. Did you notice at the start of the game that all the Vault Hunters were on that train? All the survivors are in your group. Based on my Steam friends, it looks like most people are playing BL2 solo. You may have noticed the similar fate of all but one of the Claptrap units on the planet. Okay, next joke and/or explosion, go!