Do you recommend antibiotics for your kid?

Actually you're wrong in one thing: It's not that antibiotics weaken a person's immune system, rather when we use them thoughtlessly (children and adults both) we only serve to press bacteria into developing a resistance to antibiotics. That's how killer bacteria like the super resistant flesh eating bacteria "MERSA" were created.

You're right in the sense that we shouldn't take antibiotics for a common cold, it's best to use other methods in that case, including anti-inflammatory meds or natural anti-inflammatory concoctions. In many countries of EU strong antibiotics are not given out without prescription, so people won't shove down antibiotics like candy.
There are also restrictions about prescribing antibiotics that are shown to produce sever side-effects to children or unborn-children and many are discontinued if deemed more dangerous than beneficial, unlike the US where pharmaceutical industries are only mildly regulated by the FDA.