Usually I strong-upvote when I feel like a post made something click for me, or that it's very important and deserves more eyeballs. I weak-upvote well-written posts which taught me something new in a non-boring way. 

As an author, my model of this is also impoverished. I'm frequently surprised by posts getting more or less attention than I expected.

For me, it boils down to being useful.

For something to be useful, it first has to be true. From there, there's a bunch of different ways for a post to close the gap and be something that I find useful. Maybe it teaches me how to be happy. Maybe it teaches something about rationality. Maybe it teaches me something about how the world works.

I am mostly interested in the meta. By that I mean how people get their points across or how do they developp their ideas etc.

LW is full of very interesting writing styles and approaches to questions. It interests me usually more than the subject of the question.

Otherwise : anything related to AI or how to think ends up in my reading queue.

My bar for a normal upvote is pretty low. Sometimes I even upvote somewhat low quality posts from new authors if I think they actually tried + seems like they could get better with some encouragement.

Strong upvote is for a post that hits most of: useful, interesting, well written, credible and surprising.

A bulleted list of answers others have written:

• Generates a new insight (TurnTrout)
• Is good for something (adamzerner)
• Shows its work (bvxn)
• Ties up its loose ends (curi)
• Resolves a disagreement (curi)
• Shows effort (Alexei)
• Well-written (Alexei)
• Surprising (Alexei)
• Credible (Alexei)
• Summarize work (me)

And certain topical interests which LW is a topos for:

• Cognition
• AI
• Self-improvement

I'm throwing in that I like posts and comments that compress knowledge (such as this).

My further two cents are that what people answer here will be somewhat unrepresentative. The answers will be a certain set of ideal practices which your answerers may not actually implement and even if they did, they might not represent the community at large. The honest answer to your question is probably data-driven; by scraping the site you could generate a better predictive model of what content actually gets upvotes than people will tell you here.

But nevertheless there is value to your question. The idealized picture you'll get is in fact the picture of the ideal you want. If you take onboard people's best-case answers, you'll make stuff that the most engaged people want the most of, and that will contribute to a making better community overall.

The main issue for me to write comments is whether I think discussion to a conclusion is available. Rationalists can't just agree to disagree, but in practice almost all discussions end without agreement and without explanation of reasons for ending the discussion by the party choosing to end the discussion. Just like at most other forums, most conversations seem to have short time limits which are very hard to override regardless of the content of the discussion.

I'm interested in things like finding and addressing double cruxes and otherwise getting some disagreements resolved. I want conversations where at least one of us learns something significant. I don't like for us each to give a few initial arguments and then stop talking. Generally I've already heard the first few things that other people say (and often vice versa too), so the value in the conversation mostly comes later. (The initial part of the discussion where you briefly say your position mostly isn't skippable. There are too many common positions, that I've heard before, for me to just guess what you think and jump straight into the new stuff.)

I occasionally write comments even without an expectation of substantive discussion. That's mostly because I'm interested in the topic and can use writing to help improve my own thoughts.

For me, it's all about getting more posts on that topic. A post could be bad in terms of text quality. It could be "false" or badly reasoned. But if I consider the topic underrated I will upvote it.