I find your question quite difficult to answer. There are a lot of mangas to choose from but most of them are not really comparable.
I cant really compare shonen mangas like One Piece or Naruto, written for young males to seinens like Berserk or Vagabond, written for adults. The shonens can also divided in different sub-genres, for example, battle mangas like One Piece, sports mangas like Hajime no Ippo, sci fi mangas etc.
I also find it difficult to compare mangas such as One Piece, which has been serialized over a couple of decades against Death Note, which was serialized for only 3-4 years. The plot, number of characters, world building dramatically differs between mangas with 100+ volumes (One Piece) and 12 volumes (Death Note).
Its better to compare One Piece with shonens like Naruto, Bleach, Fairy Tail, Toriko, Black Clover, Nanatsu no Taizai, Dragonball, Hero Academia, Magi, HxH etc. Out of these the only two on a par with One Piece are Naruto and HxH. The new big 3 cant hold a candle to One Piece.
Naruto till the end of Pain arc is better than One Piece in my humble opinion. Overall One Piece is better because the 4th shinobi war of Naruto was shit. HxH is tricky, I think it has a slight edge over One Piece. However, for weekly reading One Piece is better than HxH:
I understand the flaws of One Piece and Oda. But why are you guys acting like Togashi is a perfect mangaka? Go to any HxH forums (if they exist) and see how miserable their fans are. I remember the HxH fans of Narutoforums started to comment on One Piece (typically they came to vent their frustrations) because there was no HxH chapters, lol.
To Oda's credit, he at least publish content regularly, while lazy fuck Togashi takes 2-3 years of break to come up with a good storyline. That doesn't always work though, as the current arc of HxH seems as bad as Dressrosa tbh, a huge number of characters with no real purpose.
Dont get me started on HxH drawing. In many occasions, Togashi draws a small panel and writes an essay as if it's a novel, not a manga. Its almost like a punishment to read those chapters. I havent read Chimera ant arc weekly, Thank God, I have heard from HxH fans they had to endure such abominations as art during the weekly release which were later improved in the main volume:
We should be thankful that Oda is publishing One Piece quite regularly compared to HxH.
Kingdom is a mix of shonen and seinen, so it is actually comparable to One Piece. I have been reading Kingdom long before it became so popular. I love the manga and I think its on a par with One Piece. But I didnt like the recent arc of Kingdom and would place One Piece slightly above.
TL DR: The answer is No. You cant really find any battle shonen better than One Piece for weekly reading.
Just a few suggestions here, if you are looking for something worth reading:
My list will be based on how much I enjoy reading the manga only and without taking the anime into consideration:
1. One Piece
2. Kingdom
3. Berserk
4. Slam Dunk
5. Rurouni Kenshin (I started with the anime, it could be higher otherwise)
6. Baki
7. Breaker (technically a manhwa)
8. Gamaran
9. Vagabond
10. Hajime no Ippo
Honourable mention: Kengan Asura, One Punch Man, Vinland Saga
The mangas that didnt qualify because I enjoy the anime more OR I haven't finished the manga completely are:
Naruto, Hunter x Hunter, Bleach, Death Note, FMA brotherhood, Gintama, Jojo, KnB, Hitman Reborn, Inuyasha etc