>Any idea as to what I'm doing wrong here?

You don't need to use Dynamic SQL to parameterize a predicate in the WHERE clause.

CREATE PROCEDURE  up_CountRecordsforBranch
                  @BranchID             varchar(3),
    	          @TotalCount           int output
AS

SET NOCOUNT ON

DECLARE  @CurrentCount  int

Set  @CurrentCount = 0

set @CurrentCount = (select count(*) from GLDetails where CUBranchVC = @branchID)
set @Totalount = @TotalCount + @CurrentCount

set @CurrentCount = (select count(*) from TransactionDetails where CUBranchVC = @BranchID)
set @TotalCount = @TotalCount + @CurrentCount
	
GO

-Mike