“Thy edge should blunter be than appetite”
'Edge' here means the keen cutting sharpness of desire — the same metaphor that makes a hungry appetite feel 'sharp.' The speaker argues that love should not let its edge grow duller than ordinary appetite does, since appetite, though fed today, naturally sharpens again by tomorrow.
“by feeding is allay'd, To-morrow sharpened in his former might”
'Allay'd' means quieted or appeased — the hunger of appetite is calmed by eating, only to return sharper the next day. The pronoun 'his' refers to 'appetite' (a masculine noun in Elizabethan English), not to any person. The speaker uses this daily rhythm of appetite as the model love should follow: satisfied today, renewed tomorrow.
“even till they wink with fulness”
'Wink' means to close the eyes, not to blink one eye as in modern usage. The 'hungry eyes' close in satiation when they have seen (fed on) the beloved's face to the point of fullness. The speaker then warns love not to 'kill / The spirit of love, with a perpetual dulness' — a permanent satiation is death to desire.
“call it winter, which being full of care, Makes summer's welcome, thrice more wished, more rare”
The couplet offers a second, compressed analogy for the 'sad interim' of separation: call it winter, whose hardship and 'care' (anxious suffering) makes summer's return 'thrice more wished' — three times as longed-for — and 'more rare' (more precious, more unusual). Rarity and scarcity increase value; absence does the same for the beloved's presence.