<big> was removed in HTML5, however it is prevalent in wikitext (included in VisualEditor and WikiEditor toolbars) and easy for editors to use. As of rGPARbc46bcb16105: Linter: Fix obsolete tags linting + ignore BIG, Parsoid/Linter no longer warn about <big> being deprecated.
We should consider rewriting these tags to use a <span> with the appropriate styling. An extension tag won't work since that has issues with PST, but I think @tstarling suggested doing it in the Sanitizer on IRC. This would allow <big> to continue being supported in wikitext, without outputting deprecated/obsolete HTML elements.