Star Realms for something light. Radlands for something a bit meatier.

Hive is pretty fun!

I think Splendor Duel and and Seven Wonders Duel fit that description for me. Both really well thought out and specifically two players designed card based engine building games.

Been playing a lot of cribbage lately. Not a whole lot of brain power involved, just some counting.

Morels, Jaipur, and Patchwork all fit that bill. If you want a little more meat in the game 13 Days and Eminent Domain Microcosm are a bit more thinky while still being small and lighter.

Santorini, Wizards of the Grimoire, Abalone, Rummikube, Phase 10. I'll ask the wife for more later.

Ingenious, by Reiner Knizia. Scales well up to four players and is very well balanced.

The key mechanic is that there are six colors and scores and your lowest is the one that counts most.

So it's a race to develop your colors while preventing your opponents from doing the same.

象棋 (Xiàngqí or Chinese Chess) is a two-player game that I fell in love with despite hating International Chess. It moves faster, feels more dynamic, and is one of those rare games that I suck at entirely but still love to play.

I will always love Carcassonne, plain rules or with The River expansion, but none of the others, as a quick pick-up game as well.

Some of the old Kosmos two-player games were pretty great, the standout of which was, for me, Kahuna. Kahuna in particular is a game you can set up in not time flat, play in under half an hour, has enough mindfulness that it's interesting, while not being so analytical it's like taking your work home with you.

Mr. Jack Pocket was surprisingly decent. I didn't expect a lot from it, having purchased it on a whim when I found a cheap copy, but it held out to quite a few replays.

My wife and I like Dairyman. It is a light push-your-luck dice game with a drop of engine building.

60 Second City is fun and simple, but frantic in small bursts. A game only takes about fifteen minutes.

Encounters: Battletech is great fun, and I think there are a few different themed versions. It's a push-your-luck dice game. Presumably there's an unthemed version.

Kings Kilt is fantastic

Build a pyramid of scottish clan names, murder your way to the top by eliminating a card in the pyramid and move names up from the bottom to backfill positions and place a new card on the bottom row.

Really good fun

I'm not sure it fits perfectly, but clank is one I've really enjoyed with 3 players. It shines with 3, but 2 can play as well. It's a dungeon race at its core, so there's slightly less going on with fewer players.

Another that might fit even better is wingspan/wyrmspan. They also shine with 3, but are more about your own buildup, pretty chill, and even work down to solo play.

Edit: if you like card games, especially euchre, California Jack is one I found to be pretty fun and unexpectedly interesting with two people. The scoring is a nice twist. It's a trick-taking game just like euchre, but you also tally up your cards at the end. It lends pretty well to some light strategic play. I also have to mention Golf, just because I've had a good time with it. Card games can be classic and cozy.

I’d echo the thought of those 2 player kosmo games being perfect or even ones that come in that box size. Mandala, Patchwork, Lost Cities, Battleline, Jaipur and Targi are some of our favorite 2 player only games. There are plenty of multiplayer games that play best at 2 or are least still great.

BoardGameGeek.com has lots of lists for 2 player games by weight I’d recommend checking out.

Monopoly Deal is one of our favourites, you can scale it up and down easily, it's funny, and doesn't take a ton of set up time or have a steep learning curve.