超過 and 過剰: exceeding a limit and exceeding what is needed
Compare exceeding a weight limit with excessive packaging, separating a numerical restriction from a purpose-based assessment.
Exceeding a stated restriction
超過, read ちょうか, means exceeding a standard or limit. 荷物の重さが制限を超過したため、追加料金を払った。 reports paying an additional charge because the load exceeded a weight limit.
With a five-kilogram limit and an actual weight of six kilograms, the excess is one kilogram. Separate the limit, actual weight, and excess.
An amount excessive for a purpose
過剰, read かじょう, describes exceeding what is needed. 過剰な包装を減らすため、簡易な箱に変更した。 reports switching to a simple box to reduce excessive packaging.
It identifies the purpose behind a packaging assessment without stating that a fixed weight restriction was violated. Context supplies the assessment standard.
Assessments that may overlap
A load over a limit might also be assessed as excessive for a purpose. The words can apply to the same object rather than naming mutually exclusive states.
制限は超過していませんが、包装は過剰です。 says that the limit has not been exceeded but the packaging is excessive. Compliance and appropriateness are separate assessments.
Is the excess six kilograms for a six-kilogram load under a five-kilogram limit?
Show the answer and why
No. Six kilograms is the total weight; the excess is one kilogram.