牵绊 has a softer, more emotional flavor than the harsh 束缚 (shùfù, fetter). It frequently shows up in song lyrics and romance novels — describes the loving-but-limiting pull of family, partners, or attachments.
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牵 (to pull by a rope) + 绊 (to trip up): something tugging at you from one side while tangling your feet from the other. The image is gentle restraint, not chains.
