One half is a little less than kind
The other is likely to ease your mind
I’m a 6-letter noun
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I'm guessing that the answer is
a nap (short sleep) may ease your mind, and "a little less than kind" presumably refers to "A little more than kin, and less than kind" from Hamlet. Not sure about "Feed me less to use me more" but maybe it's something to do with a napkin being able to be used more if less food is deposited onto it.