嗜 implies an intense, often excessive fondness. Common compounds: 嗜好 (hobby/addiction), 嗜血 (bloodthirsty), 嗜酒 (alcoholism). It carries a stronger connotation than 喜欢 (to like).
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嗜 is literary and formal. In casual speech, people would say 特别爱 (really love) or 上瘾 (addicted) instead.
Mouth on the left ties 嗜 to oral indulgence - eating, drinking, chewing, savouring. The radical is a strong semantic clue: an addiction or strong fondness usually starts as something one cannot stop putting in one's mouth.
Provides the sound, drifting from qí to shì along a regular Old Chinese pattern. The elder meaning is unrelated, though one can romanticise old habits as the deepest cravings - a memory hook for the mouth-plus-elder shape.
