Left raise-hand radical anchors 拄 in the manual-action family - here a planting motion, leaning one's weight on a stick or staff. The hand carries the active verb force: 拄拐 lean on a cane, 拄着伞 to lean on an umbrella.
Right 主 supplies the sound - zhǔ carried over without change. 主 originally depicted an oil-lamp flame on a stand, and that "standing upright" image dovetails with the meaning of leaning on a staff. Same phonetic family appears in 住 to live, 注 to pour, 柱 pillar.