To perceive why individuals love weapon system Art Online, one needs to understand the context of on-line play once the series was created.
When people today talk about online gaming, they are more likely to think of Dota and League of Legends. But when Sword Art Online was created (in 2009 for light novels and in 2012 for anime series), online gaming had different beasts—World of Warcraft in the West and Ragnarok Online in Asia. The theme of Sword Art Online hasn't aged very well as online gaming evolved from escapism by society's misfits into a global e-sports phenomenon.
I was a World of Warcraft Endgame player for almost three years and absolutely loved Sword Art Online. As one of the top ranked players on my server, I was able to relate to Kirito's experiences:
Bragging rights There was pressure to carry out a boss raid well enough to defeat the other guilds (like when the Ankara Liberation Force tried to claim the before The Glam Eyes in Episode 9). That means taking the time to make sure your character has the best equipment (like when Kirito and Lisbeth tried too hard to get the raw material for Dark Repulsar in Episode 7).
Daily Grind It was not uncommon to camp in a small area for hours on end to receive a rarity drop from a rare animal (such as when Kirito waited in episode 3 for Nicholas the Renegade to revive Sachi. his item may be dropped). But that does not suggest you cannot experience the arena for its easy pleasures (like while Kirito went fishing in episode 13) world exploration. The fun of meeting new people (like when Asuna joined Sleeping Nights in season two) and being able to spend time completing world quests together (like Kirito going after the Holy Sword Excalibur in season two).
Confrontation also, players are constantly reminded that MMORPGs are not only player-versus-environment (PvE) games, but also player-versus-player (PvP). There were turf wars between different factions (such as the clash with Salamanders in Episode 20) and people who played solely for the PvP aspect of the game (such as the Laughing Coffin Guild in the first season).
Sword Art Online was the perfect encapsulation of the MMORPG experience for anyone who has ever invested a decent amount of money in playing one.
The cast and animators at A-1 Pictures made sure they capture the majesty of fantasy environments in the top MMORPGs. Composer Yuki Kajiura also reprized the orchestral soundtrack that defined great MMORPGs. Even the theme song, such as Luna Haruna's "Overfly", fits well with the theme of the series. (I personally think that ALfheim Online's portrayal was the best of all the games featured in the series.)
When Sword Art Online writer Reiki Kawahara visited Seattle in 2013 to attend Sakura-Con, I was able to ask him for some resemblance to an actual MMORPG. True, he revealed that he was originally inspired by games like Ultima Online, which also inspired World of Warcraft. Kawahara was an avid player of MMORPGs and played many different games. (I believe Kirito's deus ex mechanic ability to end both Sword Art Online and Elfheim Online events is inspired by Ultima Online.)
MMORPGs were immersive environments that required the full investment of players, and the beauty of that world was exactly what Sword Art Online was trying to convey. It may not attract as many people today, but it certainly appeals to former MMORPG players.