着
zhe
着 is a paused frame, not an action
The picture You hit pause on a video. The motion has stopped, but the picture stays up on the screen. 着 never crossed the line and leaves the picture standing; 了 crossed it and left things changed.
Where the picture shows up in 着
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left standing open
门开着，进来吧。
mén kāi zhe, jìnlái ba
The door is open, come on in.
The door stands wide, holding its angle even as the draft pushes at it.
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held in the hand
他手里拿着一杯咖啡。
tā shǒu lǐ ná zhe yì bēi kāfēi
He has a cup of coffee in his hand.
The hand with the coffee is frozen like a photograph; the cup goes neither up nor down.
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one picture behind another
她笑着说了声谢谢。
tā xiào zhe shuō le shēng xièxie
She said thanks with a smile.
The smile stays lit like a backdrop, and only the words thank you come out over it.
The verb before 着 is only the backdrop; the verb after it is what she actually did, which is say thanks.
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keep it that way
等着，我马上来。
děng zhe, wǒ mǎshàng lái
Stay put, I will be right there.
Both feet stay glued to the spot where they were, not one step moved.
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left lying there
桌子上放着一份合同。
zhuōzi shang fàng zhe yí fèn hétong
There is a contract lying on the desk.
The contract put down in the morning is untouched, still in the same place in the afternoon.
All of it in one picture
The door keeps its angle, the cup keeps its place in the hand, the smile stays lit while the words come out over it, the feet stay glued down, and the contract stays where it was left. None of these say someone is doing something; they say the picture has not been wiped away. A verb with 着 is a still frame, not moving footage. And because it is a still frame, another action can be laid on top of it.