weight limit for air travel baggage?

how much weight is allowed per suitcase on planes

It varies by airline carrier. When I recently flew Northwest, the limit was 50 lbs. for one checked in bag. I was also allowed to take a carry on. If your bag was over 50lbs. there was a fee. But the bag still had to be less than 75 lbs. An extra checked in bag was subject to a fee though I forget what that was.

Well it depends on the airline, and domestic or international. It also depends on the type of ticket you have booked.

Usually 20-25 Kg and last time I checked 10-14 Kg carry on luggage (but they rarely weight carry on luggage so you can put all the heavy stuff in there)

In times past you could get away with being a little over weight, but with rising fuel costs they will hit you with excess luggage fees. Call the airline and ask.

Hold baggage.
The maximum weight depends on the airline. British Airways will allow you 22kg but most will permit 20kg. This is the total per person so there is no hope of having two 22kg cases and getting them on for free.
Sometimes it is possible to buy an extra allowance. This is usually expensive (around £12/kilo).

If you are travelling with someone else then some airlines, like BA, will allow you to distribute your joint allowance between you. This means that one bag may be slightly more than 22kg and the other may be less, but the total must not exceed 44kg and no single bag must be heavier than 30kg. Not all airlines will permit this sharing of allowance and they insist that each bag is bleow their limit. For example - no single bag may exceed 20kg on Easyjet unless you pay a high excess baggage charge.

Cabin baggage.
This is usually limited to One Bag per person. The bag is limited by size rathr than weight because it has to fit the overhead locker. If the check in attandent thinks that your cabin bag is going to be dangerously heavy (i.e. that it would cause serious injury if it fell out and hit someone) . The cabin bag sizes are quite small because they must fit the locker. At most check-in queues there are cages for you to check the size of your bag. Anything too big or too heavy must go in the hold.

It varies according to the airline you're using, but most limits are about 20Kgs per passenger, any extra weight should require extra fees. I think that you can take up to 8Kgs of hand luggage with on board though.