This is the 18186th most frequent Russian word.
чаечек
"Diminutive form of 'чаек,' meaning 'little seagull.'"
Here, 'чаечек' is used as a diminutive form of 'tea' to make the sentence sound more friendly and casual.
Ты бы не хотел чаечек на завтрак?
Would you like a little tea for breakfast?
'Чаечек' here adds a sense of coziness and warmth to the scene, emphasizing the relaxed atmosphere.
После долгого дня мы собрались на кухне и пили чаечек с булочками.
After a long day, we gathered in the kitchen and drank a little tea with buns.
In this instance, 'чаечек' implies both affection and care put into the tea preparation, enhancing its sentimental value.