'unmetered' originates from English prefix 'un-' plus the past-participle/adjectival form 'metered', where 'un-' meant 'not' and 'metered' derives from 'meter' (from Greek 'metron' via Latin/French).

'meter' comes from Greek 'metron' ('measure') through Latin/French into Middle English as 'metre'/'meter'; English formed the participial/adjectival 'metered' (measured by a meter), and the negative form 'un-' + 'metered' produced 'unmetered'.

Initially related to being literally 'measured by a meter' (or not); over time the negative form 'unmetered' retained the literal sense but also acquired a specialized sense in services/telecom meaning 'not subject to usage-based billing' (effectively 'unlimited' in that context).