Go underground for some time maybe.....

Why you are calling "weather" what is a pollution problem ? There's nothing you can do apart from moving out of Beijing.

Yep, there's not much you can do about pollution other than buy a space suit  or move.

So what can you do? Firstly, if all this is a real concern for you, reconsider whether China is the right choice for you. Air pollution is going to remain an issue in China for many years to come - the best you can do is limit your own exposure.

Here are a few practical steps you can take:

1. Monitor the AQI and levels of PM 2.5 particles (fine particles which can enter the bloodstream). Download an AQI-monitoring app for your phone, tablet or computer to keep an eye on pollution levels in your area. See our article on "Apps for Tracking Pollution" for recommendations.

2. When the AQI is above 200, try to limit the time you (and your children) spend outdoors. Exercise outdoors is inadvisable under these conditions.

3. If you must go outside during periods of heavy pollution, wear an N95-rated pollution mask (these can block up to 95% of fine PM 2.5 particles), hat (if temperature allows), and with minimal skin exposed. Avoid busy roads as far as possible to avoid breathing in fumes from traffic.

4. Keep doors and windows closed as much as possible indoors.

5. Remember that even with doors and windows closed, the air you're breathing indoors still contains many of the particles that can cause harm. Use an air purifier at home and in your office to keep the air you're breathing indoors as clean as possible. A variety of options are available at different price points, from the "DIY" filters sold from around 200 yuan by Smart Air (http://smartairfilters.com/) to the top-end machines sold by the likes of IQ Air (http://www.iqair-china.com/en_gb/) and Blueair (http://www.blueair.cn/en/index.asp).

Finally, pay attention to what you're eating - a healthy diet cannot make pollution go away, but it can keep your body and immune system strong.

You could learn more advice here http://onestop.globaltimes.cn/pollution-in-china-an-introduction/

Get an air purifier+humidifier for your room and try to get a decent amount of vitamin C regularly, but yea perhaps the best solution is to move out. I think the air pollution is the least of your worries, all of those pollution will eventually go down and contaminate the soil/water around Beijing (I assume thats where you get the food and water for Beijing).

Lol... since when did pollution become the "weather"?

I just really don't like the sound of that because it makes it sound like it is nobody's fault (like weather) when it clearly IS. Can we stop tornadoes? Nope. Can we stop earthquakes? Nope. Can we stop pollution? Yes. 

Know what I mean? But to answer your question... I would just plain leave. 

This is pollution mate, not natural weather, Beijing has never been covered by a thick fog in history, unlike Chengdu or Chongqing for e.g., only by smog recently.

Not that the government is not doing any effort, when the pollution started to reach them and their families (never considered it before) they ordered to move the factories further from the city, kudos to them 

I solved the problem by moving away, Beijing's airpocalypse during winter (yes because it's much worse in winter you will see) is mostly due to heating that require more coal to produce electricity, this is what happen when 20 millions people (I think that's Beijing's population) turn on their AC heater at the same time.