As the fuel price is going up passengers are loosing on their weight on carry on luggage and 
baggage allowence. Also transport workers unions made to the baggage size to a limited size. Although some Air lines are giving advantage to passengers to stay in the market.
Most of the Airports have a standard box near to the ticketing counter to check wether your carry on luggage fit in to it and to check the weight. this is to ensure your carry-on luggage will fit in the overhead bin or under the seat in front of you.
Regarding the Baggage, this may differ from Airlines and the distance you travel. Normally this is between 20Kg - 40Kg. You have to verify this with your travel agent when you buy your air ticket.
The normal Air line maximum dimensions of carry on luggage is 45 linear in/115 cm (total: length + width + height) Maximum weight of carry on luggage: 15 lb/7 kg
Baggage Allowance.
Baggage allowance normally 2 pieces.
Maximum dimensions is 62 linear inches/157 cm (Total: length + width + height)
Don't carry more than the allowed weight in baggage. The Airline will charge you for the excess weight. This may increase according to the distance. (if you are lucky, some time they may allow you to carry some kilos of excess luggage free of charge).
At the check in counter get your hand luggage Tag and put it on your bag.
Once you hand over the baggage they will staple the baggage number tags on your ticket.
If you are travelling as a family you can weigh all the baggages together and and get the tags on one ticket. This will help you to over come little of the over weight.