Kim Kardashian & Pete Davidson Enjoy Early Valentine's Day Date Night

Kanye West may consider himself at war with Pete Davidson and Kim Kardashian -- but the couple clearly isn't sweating his barbs ... 'cause they're feeling the love in the Big Apple.

PD and Kim were seen grabbing a bite Saturday night in Brooklyn, arriving at a high-end Italian joint called Lilia ... walking up hand-in-hand for what was apparently an early date night head of Valentine's Day on Monday.

As you can see ... they were totally grinning as paps fired away and followed them up to their private tent, where they eventually went in and broke bread just the two of them.

Eventually, they left and beelined it for their waiting SUV, where Pete helped Kim into the back ... and then walked around the other side to join her. They were both rocking shades for this outing -- and they each looked sharp and totally in lockstep coming to and from.

Of course, them standing shoulder to shoulder like this was happening right in the thick of Kim's estranged husband going off the rails in post after post after post ... taking shots at Kid Cudi, and Pete by extension.

The posting has yet to cease, even a full day later ... if anything, they've only gotten worse and much more personal, with no signs of slowing down.

Ye's latest attack is yet another open plea for reconciliation with Kim -- in which he points out that he's trending above the Super Bowl right now ... and, indeed, he's right up there.

KW says he hopes everybody who's married holds their spouse close and lets them know how much they love them, because it can all be over in a flash. He then takes a shot at Pete, whom he calls "Skete," by saying there's always someone like him lurking about.