Physics pedant alert: spring weighing scales and balances are the classic way of explaining the difference between weight and mass at GCSE level. You do actually weigh yourself (establish the applied force rather than the mass, via Hooke's law) on a bathroom scale. Top Viz weight loss tip - take your bathroom scales to the moon and you will instantly weigh less than you did on earth.
But yes, the point stands: everyday language practices are not transferrable to science.
Everyday language is now a complete clusterfuck of confusion where "gender" can mean
(1) which definite article a noun takes in a foreign language (probably not relevant to most of these discussions)
(2) shorthand within social sciences for the set of sexist stereotypes about dress, appearance and activities appropriate to one sex or the other so deeply embedded in a given culture (and variable across cultures) that the people within the culture often don't even realise they're there
(3) a nebulous inner feeling of "femaleness" or "maleness" or "in-between-ness" which some people say they experience (but which curiously, when pressed, always seems ultimately to boil down to the sexist stereotypes of point 2 above - though in fairness that could be to do with the issue that we are all embedded in our culture to the extent that we don't even see it's there and it's impossible to explain things without using language which is embedded in and expressive of this culture).
(4) as a synonym for biological sex from people to coy to say "sex" in case someone confuses that with the act of fucking.
If you're talking about biological sex in the biological/medical literature, you really should say "sex" (with caveats about DSDs where appropriate). After all, a textbook on working out blood test levels for deciding whether to commence kidney dialysis depends crucially on sex, not on internally sensed gender (see for example, the tragic case of a transman, i.e. someone born biologically female and now "presenting as male" in America, who was in fact in end-stage kidney failure had the bloods been correctly assessed as female results, but wasn't given dialysis because the case was treated in accordance with the appropriate test results in someone biologically male).