In the early to mid 1970’s, the “Rough Drafts” for Star Wars, we had the Jedi Kane Starkiller being a father to two children, Deak and Annikin:
https://starwars.fandom.com/wiki/Kane_Starkiller & https://starwars.fandom.com/wiki/The_Star_Wars_1
and like Superweapon VII, I think the later drafts also had some mention of Jedi having families or offspring too.
In the official 1983 Return of the Jedi novelization, by James Kahn, we have Ben Kenobi telling Luke that Owen was his own brother:
In the official licensed 1995 Premiere Limited set of the Star Wars Customizable Card Game, released by Decipher, it is stated that Owen Lars is the “brother of Obi-Wan Kenobi”:
https://starwars.fandom.com/wiki/Premiere_Limited & https://starwars.fandom.com/wiki/Owen_(Kenobi)
In the Tales of the Jedi comic books, from 1993 to 1998, Jedi had families and children too. Notably Nomi Sunrider, who was wife of a Jedi, became a Jedi herself, and her daughter Vima, also became a Jedi. The family had a personal droid, A-3DO, so I think that may count as a “possession” too?
Kam and Tionne Solusar, both Jedi, were already married by “Star Wars: Union” comics (1999-2000) and had been married for some prior to Luke to Mara Jade getting married to each other. Kam was the son of Ranik Solusar, a Jedi Master slain by Darth Vader.
https://starwars.fandom.com/wiki/Kam_Solusar & https://starwars.fandom.com/wiki/Tionne_Solusar
Luke marrying Mara Jade in “Star Wars: Union” comics (1999-2000) (note the red lightsaber in the image below!): https://starwars.fandom.com/wiki/Wedding_of_Luke_Skywalker_and_Mara_Jade - and would obviously have a child (Ben)
Corran Horn and Mirax Terrik were married sometime after the Bacta War and before 1998’s “I, Jedi”, where Corran had to further improve his force skills in order to save his wife:
They had 2 children, when Corran was a Jedi Master.
Corran’s grandfather was a Jedi too:
Nejaa Halcyon, a Jedi Master, grandfather of Corran Horn - https://starwars.fandom.com/wiki/Nejaa_Halcyon
Valin Horn, a Jedi knight, son of Corran Horn - https://starwars.fandom.com/wiki/Valin_Horn
Jysella Horn, a Jedi knight, daughter of Corran Horn - https://starwars.fandom.com/wiki/Jysella_Horn
Quinlan Vos had a relationship with Khaleen Hentz. They had a child, named Korto Vos.
https://starwars.fandom.com/wiki/Quinlan_Vos/Legends & https://starwars.fandom.com/wiki/Khaleen_Hentz
Kento and Mallie Marek were both Jedi, and had a son, Galen Marek, aka “Starkiller” (in the 2007 “The Force Unleashed” videogame, that George Lucas actually considered part of the main Saga story).
We see Galen father, Kento Marek, at the start of The Force Unleashed video game. We don’t see Galen’s mother as she died before the events of the game:
https://starwars.fandom.com/wiki/Kento_Marek & https://starwars.fandom.com/wiki/Mallie_Marek
Jedi Master Thracia Cho Leem married multiple times and had several children. She resigned from the Jedi Order without explanation prior to the Clone Wars (in 2000’s Rogue Planet novel?)
Jedi Knights Callista Ming and Geith Eris also had a relationship, in the Clone Wars era:
https://starwars.fandom.com/wiki/Geith_Eris & https://starwars.fandom.com/wiki/Callista_Ming#Personality_and_traits
In the TOR era (and video game):
Kira Carsen was a Jedi, whose parents were both Sith. https://starwars.fandom.com/wiki/Kira_Carsen
https://starwars.fandom.com/wiki/Kira_Carsen's_father & https://starwars.fandom.com/wiki/Kira_Carsen's_mother
In the game you can marry, or have a romantic relationship, with your Jedi apprentices. One of whom is Kira Carsen.
^ The same applying to Nadia Grell:
‘Nadia Grell is a companion character for the Jedi Consular class of Star Wars: The Old Republic. In the original class storyline, she was a romance option only for male player characters. After she returned in the “Jedi Under Siege” update, she became a romance option for all Jedi Consulars regardless of gender.’
Lana Beniko is a similar Dark/Sith side character: https://starwars.fandom.com/wiki/Lana_Beniko#Behind_the_scenes
In the 2014 Rebels animated series, set just before the OT, Jedi Knight Kanan Jarrus marries fellow rebel Hera Syndulla and they raise a child named Jacen Syndulla (who has force abilities).
Jedi Masters T’ra Saa and Tholme fell in love, had a relationship, but ultimately did not get married.
https://starwars.fandom.com/wiki/T'ra_Saa & https://starwars.fandom.com/wiki/Tholme/Legends
As Vladius posted above: “All the source material before Attack of the Clones suggests Jedi with families and children.”
I think many of us before Episode II thought it was just natural that a number of the Jedi did have partners, families and children, had their own homes or dwellings, and had some possessions, like droids, and so on.
Then George Lucas just thought he needed to create a “forbidden love” subplot in AOTC, while lacking the skill to coherently write it. And he unfortunately didn’t get in someone who could. For some reason, this 2002-ish invented “forbidden love” rule has stuck, in the main.