In fact time always "moves" at the same speed to any given observer. It appears to move at different speeds to an external observer, but you cannot experience slowed time as such - except in the sense that you might observe external clocks ran faster than the watch you had your wrist.
An attempt to explain: The supposition - very strongly supported by the experimental evidence (the latest discovery of gravity waves being the jewel in the crown) is that we live in a four dimensional spacetime. An individual always experiences time as "moving" at a constant speed, but as has been remarked by others, externally gravity appears to add curvature to the "straight line" we are moving along on the time dimension and so we "gain distance" in this direction more slowly when seen externally.
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