Latin officium named duty or service, behind the adjective officiosus and English officious. Older English could use officious approvingly for being dutiful. The familiar modern use instead suggests unwanted or intrusive help.
The Latin adjective already had negative as well as positive uses. The contrast between dutiful and meddling English senses does not mean all negative associations began in English.
Source
Merriam-Webster: officiousArchaic sense 3b and the first-use record support dutiful; Word History records both positive and pejorative Latin senses.