A surface to air missile doesn’t need to go to space, so it has a relatively short burn. As you burn fuel the remaining vehicle and fuel is lighter, so acceleration increases (for the same amount of thrust).
A space-bound rocket is designed to have a liftoff thrust to weight to just get off the pad when full. As it burns and gets lighter the thrust to weight increases. For sending humans up the maximum acceleration is limited to typically 3 G.
A missile doesn’t need that limit.
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