A basic concept might make things clear
-- UA has a check bag fee structure
-- For various reasons (elite status, credit card primary cardholder, premium cabin, ticket bag allowance, ....) certain fees, such as first or more bags may be waived / with up to 70 lbs allowed on the waived bags in some cases
--
that waiver does not affect the rest bag fee structure -- such as if the first bag is waived, the second bag price is unchanged
-- there is a general North American fee structure (Mex is slightly different) and International (first bad fee waived except for Basic Economy -- a few countries, such as Brazil, China, ... may have a second bag waiver
North American (not Mex)
1st bag - $30
2nd bag - $40
Third bag and Any Additional --$150 per bag
up to 62.0 linear inches (157 cm) and 50.0 lbs (23 kgs)
Oversized Bags - $200 extra per bag
from 63.0 to 115.0 linear inches (160 to 292 cm)
Bags which exceed 115 linear inches (292 cm) and 100 lbs. (45 kg) will not be accepted as checked baggage.
Overweight Bags
from 51.0 to 70.0 lbs (24 to 32 kg) $100 extra per bag
from 71.0 to 100.0 lbs (33 to 45 kg) $200 extra per bag
Standard Internation
1st bag - $60
2nd bag - $100
Third bag and Any Additional --$200 per bag
up to 62.0 linear inches (157 cm) and 50.0 lbs (23 kgs)
Oversized Bags - $200 extra per bag
from 63.0 to 115.0 linear inches (160 to 292 cm)
Bags which exceed 115 linear inches (292 cm) and 100 lbs. (45 kg) will not be accepted as checked baggage.
Overweight Bags
from 51.0 to 70.0 lbs (24 to 32 kg) $200 extra per bag
from 71.0 to 100.0 lbs (33 to 45 kg) $200 extra per bag
Fees are charged at check-in and will apply for each direction of travel (generally each full checkin, note rechecking after customs is not a "checkin")
As there are certain route exceptions, always best to check with
UA Baggage calculator
Additionally, a few routes have standard / seasonal
Excess Baggage Embargo
This UA's fee structure when checking in with UA. Checking in with another carrier adds additional complexity (depending if the ticket is under US DOT rules or not)