Lately it seems that I end up knowing more about the client's requirements than the client themselves. Does it seem very weird as a developer for this to happen?

Not.at.all.

Like @antorqs said, it's completely normal. Clients rarely know what they want and even after you go through the tough phase of buzzword translation, it often amounts to not much.

Little piece of advise: The key is, let the client know what they want and they don't know BUT make them believe it was their idea.

Once you master that manipulation technique, you can move on to let them want what YOU want and make them believe it was their idea.

@antorqs so... like... inception :)

@commanderkeen Yeah! only they're fully awake and you just want them to prefer the script to be executed once a week instead of every day because you know there won't be new data and you don't want to be checking logs for nothing ':-D

They never know, I often get called in to clients to provide a quote on a website. The meeting ends up with me firing loads of questions (I always thoroughly research the company/competitors and audience prior to such meetings), and steer away any discussion about aesthetics, at this juncture it is irrelevant. After the meeting I formulate a website brief before i quote asking them to read through and provide feedback before estimating. P.S. I never provide quotes always only estimates, there is a legal difference.

What is a price quotation?
A quotation is a fixed price offer that can't be changed once accepted by the customer. You must adhere to the quotation price even if you carry out more work than you expected. If you think this is likely to happen, it makes more sense to give an estimate. You can also specify in the quotation precisely what it covers, and situations that will lead to additional charges.

What is a price estimate?
An estimate is an educated guess at what a job may cost. It isn't binding. To account for possible unforeseen developments, you should provide several estimates based on various circumstances, including the worst-case scenario. This will prevent your customer from being surprised by the costs.

Nope. Largely because I find coding forces you to think about the edge cases.

Things they’ve either missed in their domain model, or something that emerges from their model when mapping it to the binary logic of machines.

It can be downright spooky to a client / employer when you bring these cases up, so do it at every opportunity and relish in it.