I've found where to do it -> under Health Activities in the Garmin Connect site there's an Export button top right when you select Weight. But what you get is terrible. And I can see locked threads going back nearly ten years all complaining about the same thing. Something which ought to be pretty easy for them to fix.
First off, weight entries are split across two lines. They clearly imagine that this is a handy way to group multiple weight readings in a day under one day header. It isn't, it's terrible. The majority of people who want to export their weight as a CSV are going to be opening it in Excel or some other Spreadsheet software - all of which are more than capable of sorting and grouping by day if the user wishes. But none of which find it easy to sort and manage single data entries across multiple lines. A minority of people will be wanting to use the CSV to import into some other software. For them it's even worse.
That is one of the biggest issues. The second is close behind - the date format. "Mar 1, 2024" as a text string is a royal PITA to work with. And it's explicitly a " " bounded text string in the CSV causing Excel to read it as such and be unable to treat it as a date. You could with minor work fix that except "Mar 1, 2024" is no natural date format that it has built in support for. Presumably they think this is a good way to handle both American and Rest of World date formats because you can tell the difference between 1/3/2024 (first of March in most of the world) and 3/1/2024 (first of March in the USA but 3rd of January to most other people). Again, it's not a good thing - it makes it immeasurably harder to work with. It is relatively trivial for anyone in Excel or equivalent to swap a date around to their native and almost everybody would notice that they needed to because two thirds of the date entries on average would have impossible months. Instead you get something where you have to write some sort of script or edit a file with regular expressions to bring it into order. Something that not everybody is capable of and is a nuisance even to those who can.
Frankly, splitting date and time into two columns isn't ideal either but it's a lesser nuisance. Fix the two above and things would be in a far better place. Assuming someone wants to export their weight regularly, which if someone wants to do it at all probably wants to do it more than once, and it's a painful ugly process for no good reason. There is zero chance that internally the data is stored this way. So just export it in a better format. If they're concerned about backwards compatibility (though frankly anyone who has hacked together processes to deal with this export format would probably be relieved), then they can make it an option or setting. (And default it the sane version of the export for new users).
Ten years I see posts complaining about this. For what should be a very minor change for their developers.
(I haven't even looked yet to see what horrors are lurking in the other exports. I'd love to just ask for some JSON but I know to reign in my ambition)
Please fix this, Garmin!