Shin Megami Tensei is not weeaboo-style at all, judging from what I saw. Persona, number 1 and 2 are more similar to SMT so those are less weeby. 3 and 4 are very weeby, 4 more than 3. 5, I have no idea.
AFAIK the series from 2 onwards features romance. 3 and 4 allow poligamy, 4 lets you choose whether to date a girl or not.
2's romance is apparently not as prominent and there is a gay option. The sequel to 2 (not 3, more like 2-2), I am not sure if it has romance.
SMT deals with demons and creatures, and has alignment based endings (Chaos, Law or Neutral I think). It might interest you if you like stories about occult and cruel deities.
Persona is more about human relationships, but all the games deal with them differently.
I mostly played 4 because it was the first I found in a shop and after 60 hours of YUKIKO SENPAI YOUR SERAFUKU BENTO IS SHOWING and fanservice I could not take it anymore. I kind of went in expecting evil gods and demons and creepy shit though.
I'm way late to this. I have persona 5 and I really really really really really really really really really really enjoy it. It's way darker than any of the other games, especially in terms of how you make personae now (you essentially pick which way you execute your personae for various ability cards, items, or fusions of new personae).