旁 grew from 方 'direction' under a spreading top: what fans out to all sides. It settled on the sideways ones — the flanks, the edges, the seat next to yours.
旁边 'the side' answers half of all where-questions in Chinese: 在我旁边 'next to me'. 旁人 are bystanders; 旁观 to watch from the sidelines. And the components of Chinese characters themselves are called 偏旁 — every hanzi has its sides.
Directions 方 fanning out — the space BESIDE you.
旁观者清 'the bystander sees clearly' — chess players in Chinese parks endure endless sideline advice justified by this proverb.