I've flown on almost every budget airline in Asia, but I've never had my carry-on weighted.
As for checked in luggage, consider any over the limit fees as part of the fare, it will still be cheaper than full service airline. One other thing to remember: if your trip consists of several segments on a budget airline and you are over the weight limit, you will have to pay baggage fees for each segment and this could add up to a noticeable amount.
My advice: know your ("baggage"

) limits when you plan your trip.