The Collaborative International Dictionary of English v.0.48:

Grieve \Grieve\ (gr[=e]v), v. t. [imp. & p. p. Grieved; p. pr.
   & vb. n. Grieving.] [OE. greven, OF. grever, fr. L. gravare
   to burden, oppress, fr. gravis heavy. See Grief.]
   1. To occasion grief to; to wound the sensibilities of; to
      make sorrowful; to cause to suffer; to afflict; to hurt;
      to try.
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            Grieve not the Holy Spirit of God.    --Eph. iv. 30.
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            The maidens grieved themselves at my concern.
                                                  --Cowper,
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   2. To sorrow over; as, to grieve one's fate. [R.]
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The Collaborative International Dictionary of English v.0.48:

Grieving \Griev"ing\, a.
   Sad; sorrowful; causing grief. -- n. The act of causing
   grief; the state of being grieved. -- Griev"ing*ly, adv.
   --Shak.
   [1913 Webster]

WordNet (r) 3.0 (2006):

grieving
    adj 1: sorrowful through loss or deprivation; "bereft of hope"
           [syn: bereaved, bereft, grief-stricken, grieving,
           mourning(a), sorrowing(a)]