The Collaborative International Dictionary of English v.0.48:

Beweep \Be*weep"\, v. t. [imp. & p. p. Bewept; p. pr. & vb. n.
   Beweeping.] [AS. bew?pan; pref. be- + weep.]
   To weep over; to deplore; to bedew with tears. "His timeless
   death beweeping." --Drayton.
   [1913 Webster]