What i am trying to say - paper weight does not matter. 80gsm is used because it is the thinnest paper that will reliably not get stuck in the laser printer.
Try more creamy less bleached (ultrawhite) paper. Since they are not used too much in offices they look immediately less cheap. It can be challenge to find some adjusted to laser printer formats because professional always need big sheets not small ones.
Laser printer will often look not so professional because the color is baked layer on top of the paper and it does not bleed into the paper at all. Offset printing bleeds into the paper tiny bit and it becomes part of the paper. It also has much higher resolution so it is more detailed. The difference is even bigger when you print pictures/photos. You will not get good looking pictures out of laser printer.
I've used 28 lb. and 32 lb. paper, although next time I see it I'm going to buy something thicker (36 lb. or 40 lb., assuming the pattern for commercially available thicknesses holds inductively). Thinner paper seems to be a bit too transparent, but that might be a function of the type of paper or my printer's generosity with regards to ink.
Having sewn and bound a couple of books following similar tutorials, my advice is to actually get a professional print shop to make your books if you want something of professional quality[0]. Doing it by hand is a viable hobby, but even with my continuous ink system, it's probably not economical because of the time required to bind everything together. Printing with laser is probably more expensive.
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0. If you just want to get some notes together in a reasonably permanent form, here's my three step approach to creating usable, but necessarily "beautiful" books. First, print off your book, arrange the pages, and add a blank page before the first page and after the last page. Second, align the pages carefully, ensuring that the spine is flat. Clamp the pages together, using something flat (another book, or a piece of wood works) to distribute the pressure. Finally, apply some Gorilla Glue (or similar) to the spine of the book, ensuring that the entire spine is covered but wiping away excess insofar as that is possible. Leave overnight, or until the glue cures.
The result: a surprisingly durable book from a process that takes less than 10 minutes, assuming you've got the materials handy. You can make it more presentable by adding a cover (I cut folders or cardstock into a book cover, and then glue them onto those blank pages).
Typical laserprint paper is pulp, more especially so for recycled paper. Archival stock is rag and acid-free. Back in the day, this was required for thesis and dissertation submissions, for archival purposes -- rag paper will disintegrate in time.
The other factor, though, are the size of the sheets and how they're assembled. For blunt edge-glued paperback or perfect covers, this isn't a big deal, but a printed book is produced on signatures, which are sets of sheets sewn together, and generally in quarto (four impressions per side) format (eight impressions total including the verso). Octavio is another standard, though generally for books of smaller dimensions.
You're not going to get a sewn-book feel from A4 or US Letter sized paper. And I don't think even running up to larger A3 will quite work, you're looking at about A2 for a proper quarto. Though this is out of my depth.
For example, we use uncalendered cotton stock for our letterpress printing and which has a thicker caliper for a given weight than typical, allowing better impression when printed.
Paper can be a beautiful thing when you get into it... :)