light drizzle

[Saneta]

— Now let's check on Tri-County weather. Sandy, is this rain ever going to stop?
— Yes Paul, it is. We expect it to slow to light drizzle by tomorrow morning, followed by a partly cloudy afternoon. And Wednesday and Thursday are shaping up to be partly sunny.
— That's great! Will the sun stick around for the weekend?
— It probably will. As we look at the weather map, we can see this low-pressure front moving our way is pushing out the clouds, bringing sunshine and warmer temperatures.

http://www.english-test.net/toeic/listening/a_radio_news_anchorman_asks_his_colleague_for_a_weather_update.html
Please explain:
1. check on = check out if everything is ok with weather?
2.to slow to light drizzle
3.shape up=to develop favourably?
4.stick around=stay/keep nearly?
3. push out=move out clouds from a place to the other?

Thanks ;-)

[Beeesneees]

1. check on - get a report about/ see what it is like
2. slow to light drizzle: the rain, which is currently heavy, will become lighter until it is raining very lightly.
3. at the moment, the predictions are that those days will be sunny. 'Develop favourably' is a good way of putting it.
4. stay.
5. push out - move the clouds away to a different place or even move them until they disappear.
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