OK, you [almost] got me...
Webster's US spelling ideas were to base America's English spellings on the original roots - which he took usually to be Latin - as in ***center/centrum, color/em, labor/em, honor/em etc, instead of centre, colour, labour, honour etc used in Johnson's 'English' English taken via the French...
[***actually even 'kentrus' is also a Greek word for a 'spur-point', but became the more usual meaning 'center' when in Latin]
So, although some words did originate in Greek, they had long been borrowed into Latin - like Greek's metron/metros which became Latin's meteri/metiri/metrum [both concerning 'measure']...
Words like 'metrology' do come from two Greek roots - 'measure' and study' - metron-logos...
The word 'meter' for a measuring device is [probably] from the Greek root too...
English is also proficient at wrongly combining Greek and Latin roots into single words - e.g. 'Television' [Tele=Far (Greek) + Visio=Sight (Latin)] - which might have been more logical as something like Teletheamation or Videoeminus ???
The French Commission in charge of sorting out their newfangled 'metric' system chose the word 'metre' as the length-unit's name - most say from the Greek root 'metron'>'a measure' - and it is often prefixed with Greek 'number-roots' like deca, kilo, giga, micro, nano etc, but also several Latin rooted ones like deci, centi, milli, micro [Gr&L!] etc, to confuse things completely. Latin's 'metrum' ain't that different anyway and the French did make Latin's 'center/centrum'>'centre' so why not with 'metre'? So I still believe that Webster's spelling of 'meter' for a unit of length was taken from the Latin root 'meter(i)' as it was his preferred root source - albeit perhaps mistakenly, if the French had indeed taken it from Greek as 'metre' !
To quote Webster's Dictionary directly on this: 'Meter' = Old English mēter, from Latin metrum, from Greek metron = measure, meter; Anglo-French metre, from Latin metrum...
What's in a name ? ...
I used the word 'invent' in invisible 'quotes' - they did 'make' the 'metric' system - by definition it is based on their newfangled 'metres' !
