According to https://www.easyatm.com.tw/wiki/%E4%B8%89%E5%88%86%E9%A1%8F%E8%89%B2%E4%B8%8A%E5%A4%A7%E7%B4%85 it is stated as:
字面意思:給三分顏色你就可以上大紅色,就等於不自量力,自大。明明做不到這事情都說可以做到,人家給三分顏色就想染大紅色,染得到嗎?
後來形容:人家給對方一點好處或者臉色、讚揚等,對方以為自己很了不起,其實自己一點都不行
meaning:
apparent meaning: give you 30% of color and you think can dye the cloth 100% red
used later as: people praise another person a little but and he/she thinks he/she is so awesome, but in fact the person is not that capable of doing things
but are these all the meanings? I thought I have seen it more often nowadays as,
treating a woman a little bit nicely and she thinks now she is the queen or the master of the house (or the second master of the house)
I have also seen similar versions, used in Taiwan nowadays:
得了三分顏色, 就要開染坊
getting some color, and want to open up a dye factory
but in fact it goes all the way back 400 years ago:
《金瓶梅詞話》五八:“漢子在屋裡睡了一夜兒,得了些顏色兒,就開起染坊來了。”
清·張春帆《宦海》一八:“不想這些匡主政也是個得了三分顏色,就要開染坊的朋友,見宣制軍如此,只道宣制軍怕他,一天一天的驕傲起來。”
the guys slept for a little bit; having got some color, he is opening up a dye factory
they are also people who got some color and want to open up a dye factory. Thinking the other army is afraid of them, they are becoming prouder every day