In his first appearance, they kidnap him. Every single Yoshi's Island appearance with him has him get kidnapped.
Baby Luigi does not receive any official artwork of him until his playable appearance in Mario Kart: Double Dash, 8 friggin years later.
Baby Mario then gets to appear in Mario Golf N64, Mario Tennis N64, Mario Golf GB, and Mario Tennis GB without Baby Luigi even getting referenced once. Baby Mario doesn't even receive an alternate color scheme with Baby Luigi's colors for christ's sake.
While Baby Luigi does get a sweet debut playable appearance in Double Dash, in the next console installment, he gets locked away in Mario Kart Wii in favor of putting Baby Peach instead of him. As the result, he gets no official artwork of him driving a kart. That's nice.
Yoshi's Island DS is notable for having a lot of babies usable and he is the only baby who is not usable.
Mario & Luigi: Partners in Time is mostly positive for Baby Luigi though, but I'm surprised they didn't turn him into a butt-monkey like they regularly do to Luigi in the Mario series. Even Baby Luigi sometimes abuses Luigi in that game too for fun. Baby Luigi isn't entirely scotch-free in this game, being abandoned by Luigi, getting jumped on by Baby Mario, crying a whole deal, but it's pretty par for the course for the rest of the characters too and the crying is simply part of his personality.
Baby Luigi then gets shafted in Super Smash Bros. Brawl, Mario Tennis Open, and Mario Tennis Arcade GP DX in favor of Baby friggin Peach despite that he's a veteran who's been around longer. Baby Luigi would not get a tennis and golf appearance until Mario Sports Superstars, though that game is very positive towards Baby Luigi and gave me tons of fanservice of him and was pretty much a loveletter to the only Baby Luigi fan in the planet.
Baby Luigi receives next to no acknowledgement in the Year of Luigi in 2013. Hell, the most he got was being kidnapped again in Yoshi's New Island and a mention in Luigi's Mansion: Dark Moon.
Baby Luigi's very first appearance in Mario Kart 8? This.
And the official artwork he received? This.
Baby Luigi has no animated LINE gif but eh, rejection in favor of Baby Mario is too commonplace for me to count against that (he doesn't even get a hanafuda card with him in it while Baby Mario does). Still I think it would kill them to add Baby Luigi ACTUALLY BEING WITH Baby Mario for once.
And now there's that official tweet, rubbing it in.
And now can you see why I'm grumpy all the time?