Each airline sets its own baggage allowance. Most long-haul carriers include one checked bag (23kg). Low-cost carriers charge extra. Your luggage won't transfer between separate tickets - you'll collect and recheck at connection points. Pack for the strictest airline on your route.
Each airline on your RTW itinerary has its own baggage policy, and those policies can vary significantly from one leg to the next. The practical reality is that you need to know the rules for every airline on your ticket, not just the first one.
Most full-service international carriers include at least one checked bag of 23kg (50 lbs) in economy and 2 bags in business class. But the specifics vary. Some airlines allow 30kg. Others are strict at 23kg. A few carriers, particularly low-cost or regional airlines that might appear on shorter legs, charge for any checked luggage.
The golden rule for RTW packing: identify the most restrictive airline on your itinerary and pack to that standard. If one leg is on a carrier that allows only 7kg carry-on, that's your effective limit for carry-on weight the entire trip (unless you're willing to repack at every airport).
Most experienced RTW travelers go with one carry-on bag and one checked bag. Some go carry-on only. The less you bring, the easier every airport, train station, and taxi ride becomes. A 40 to 45 liter carry-on backpack and a small daypack is a setup that works on virtually every airline and every type of ground transport.
Your AirTreks itinerary documents include baggage allowance information for each flight segment, so you'll know exactly what to expect before you leave. If you see a restrictive leg, your consultant may be able to adjust the routing to a carrier with better baggage terms, assuming the price difference is reasonable.
A few more practical tips. Weigh your bags at home before you leave. Invest in packing cubes. Bring a lightweight, compressible duffel for souvenirs you accumulate along the way. And keep anything irreplaceable (medications, passport, electronics, one change of clothes) in your carry-on, because checked bags occasionally take a detour.