In the village menu you have the option 'Show economic information' This shows which production slots the village has (something which also exists in native, but there wasn't an option to view them)
And the tax you get from the village depends on how many such production sides the village has. It also depends on which production side it is. A silver deposits for example, can generate a lot of wealth. How much wealth such production sides generate, also depends on the season. E.g. during harvesting season (currently July, August and September) grain fields generate a lot of money.
And everything is modified by prosperity: max prosperity means a bonus of 20%, low properity means a malus of even up to 80% (if 0 prosperity)
(Same holds for castles and towns)

But if you feel that any town/village or castle generates way too much money please feel free to tell it to me. The game has 48 towns more than 50 castles and more than 200 villages, so its hard to test for me

Very interesting. When you say "production slots" you mean things like "number of pottery klins", "fishing boats" or "acres of pasture", etc? Do these values change during gameplay, or are they fixed?

I'll keep an eye on abnormalities in the economy, but rents and tarrifs are so hugely variable, even in the vanilla game, that it's hard to say. Nothing massively breaking so far for me. If anything, it's surprising how little you get from cities, considering they need a big and expensive garrison. I've also noticed a couple of times, some villages paid "None" (and, no, they were not bandit-infested, I was nearby and visited it right away to check).

The one abnormality (but not to game-breaking proportions) for me was Ctesephone. I wasted the town as I took it, but the very next week it was reported as the 2nd most productive town in the world, despite prosperity being like 25. This did not seem to translate to particularly large taxes, though, and the place is perpetually plagued by never-ending bandits coming out of Arabia and Judea.

I did find a rich village! Alia, southeast of Gaza, in the middle of the desert and surrounded by hordes of bandits, comes with 14(!) silver mines, which is huge since everywhere else I checked has at most 1 or 2, and those are usually towns. But it doesn't translate into THAT much money. I get 8-15k from it. More than a regular village, but not so much that it would make a big difference in my budget.

"Very interesting. When you say "production slots" you mean things like "number of pottery klins", "fishing boats" or "acres of pasture", etc? Do these values change during gameplay, or are they fixed?" Exactly, and they usually should stay the same.
"None" that can happen if the weekly payement stuff triggers before the village was able to pay its taxes.

In TW Attila alia has a gem deposit, that's why I added a silver deposit here (I am not sure how accurate this is, I usually assigned those slots without making much research (since I don't really know where to find the sources), I rather used my common knowledge

And mesopotamia in total is quite rich, because of the dye and silk production I gave them (I thought due to silk route trade they should have that)

Even more interesting. So the fiefs don't pay on week end report day, then, and instead taxes accumulate over the week and just get distributed to you then? Would it mean that if they didn't pay one week, they will end up paying more the next week? If so, that would account for some wild variability I'm seeing (in vanilla too) in payments per week (and, sure, some of that is seasonal and controlled by other factors.

And, no, you're right on Mesopotamia having silk and Alia precious metals. I think it is reasonably balanced by being remote and infested with never-ending raiders, which is what led me to get out of Ctesephone despite its wealth. I do think it's a bit weird that cities give so little income overall, though, since they need so much to pay the garrison. Both my cities are just about breaking even, losing money some weeks and making in others with the garrison costing about 8k for each. But I haven't been watching this for very long yet, and only had three different cities so far, so I can't make a general statement, but it feels like owning a city is comparable in profitability to owning a weavery and dyeworks in that city. Which is weird considering how much harder it is to get a city than to build a business in one.

One thing I would recommend nerfing about Alia, just because it doesn't make sense, is the grain acreage. It has 40000 right now, which is the largest I've seen, and the place is in the middle of a desert.

Would it mean that if they didn't pay one week, they will end up paying more the next week?
Yes, but if the village is looted in meanwhile, you wont get any tax

So the fiefs don't pay on week end report day, then, and instead taxes accumulate over the week and just get distributed to you then?
Yes

If so, that would account for some wild variability I'm seeing (in vanilla too) in payments per week (and, sure, some of that is seasonal and controlled by other factors.

Exatly this is a vanilla thing. Taxes are accomulated over time by a weekly trigger. If the settlement is looted at the time when the trigger fires no tax will be added.

Regarding cities: The income should be quite stable over time (something between 10,000 and 20,000 with taxes and another 5,000 to 15,000 with tariffs), because their sources of income don't depend that much on season. And if you are in the heart of the Empire, you don't need a large garrison.

"but it feels like owning a city is comparable in profitability to owning a weavery and dyeworks in that city. Which is weird considering how much harder it is to get a city than to build a business in one." hm thats a good point.

"One thing I would recommend nerfing about Alia, just because it doesn't make sense, is the grain acreage. It has 40000 right now, which is the largest I've seen, and the place is in the middle of a desert." Ah, this shouldnt be the case, since its in the desert

In the current version I found fairly good results with owning mine villages in modern-day Algeria and Egypt. Both have cities with three mine villages attached to them, and the villages themselves are fairly productive.