All airlines have a weight limit for the luggage. Mostly the intercontinental flights of economy class is 23 kg/50 pounds per luggage.
Then, mostly you can just check in just 1 luggage per person. If you want to check in another luggage, the surcharge applies and at least it will be EUR 50 per piece.
If your luggage exceeds the weight limit = 23 kg, you have to take out your stuffs from your suitcase and carry with you during the flight.
Therefore I recommend to take out the heavy item, not the bulky item. Mostly the heavy ones are books. Then, do not forget that there is a limitation of liquids you can carry to the aircraft. You are allowed only 1 transparent resealable plastic bag(Ziploc) which is maximum of size of 1 liter. Then, you can put liquid or gel which is up to 100 ml inside the bag. Be aware that the volume is not the actual volume of the liquid but the volume of the container.
Finally, please do not fill up your suitcase when you are departing from your home town. You will buy many souvenirs in Japan! I recommend to maintain 1/2 of the space.