[RadioKid]

”分:BUN/FUN/PUN” is used as "minute", "divide","understand" and "portion".

In this case, it is used as a variation of "portion".

"僕の分は終わったよ:BOKU NO BUN WA OWATTA YO;I have done with my part (of the work,job or else)"

"周りの感情を吸収しやすい分" would be translated as "As he tend to feel the atmosphere around him" or "As he has ability (as a portion of property) to feel the atmosphere around him".

Does this help?