。
As of tomorrow, it will have been raining for a full week.
Literal
Tomorrow [with-で] completely 1-week rain [subject-が] continue-falling [nominalizer-事] [dative-に] become-is probably.
The で here marks tomorrow as a boundary marker for a duration accumulation — 'with tomorrow [as the marker], it will make X.' 丸々 is an emphatic 'full/entire' reduplication. 降り続く is a compound verb (降る + 続く) meaning 'continue raining.' ~ことになっている here reports a developing/fixed circumstance, and でしょう hedges it.