According to the American Psychological Association style guide, the suffixes in names such as Jr. and Sr. should not be used for in-text citations, but must be used in the reference list. Similarly, the Associated Press style guide says to use these suffixes in only the first reference.
These rules only apply to the suffixes used in names. Other suffixes, such as -ness and -wise are accepted components of the words themselves and are allowed in all writing situations. Generally speaking, the suffixes for names should be used only in formal situations or the first time a person is mentioned.