'By marriage' indicates a person has become part of your family after marrying someone related to you. My uncle by marriage always joins our family gatherings.
Pro Tip 2/3
Neutral Tone
The phrase is descriptive and neutral, without any positive or negative connotations about the relationship. My cousin by marriage has been a part of our family for years.
Pro Tip 3/3
Legal Connection
'By marriage' signals a legal or formal expansion of family, not just a social or friendly relationship. I have two sisters by marriage after my father remarried.