The other meaning of 大
We can use the adjective 大 
to emphasize what time an action took place.
to emphasize what time an action took place. Pay attention
It often has a figurative meaning.
Examples
我大半夜都没睡觉
I was up all night
wǒ dà bànyè dōu méi shuìjiào
她一大晴早就不知道忙什么去了
She didn't know what to do in the early morning
tā yí dà qíng zǎo jiù bù zhīdao máng shénme qù le
大周末的，让我睡多一点吧
Let me sleep a little longer on the weekend
dà zhōumò de, ràng wǒ shuì duō yì diǎn ba
大晚上的你在这里做什么，赶快出去！
What are you doing here at night? Get out!
dà wǎnshàng de nǐ zài zhèlǐ zuò shénme, gǎnkuài chūqù
We can also use it to emphasize that an action or phenomenon is unusual due to the time in which it’s taking place.
Examples
又大早上吃肉啊
Are you eating meat in the morning again?
yòu dà zǎoshang chī ròu a