Try these and see what improvements or otherwise they make:
CREATE INDEX IX_Edge_SessionId_EdgeID ON dbo.Edge(SessionId, EdgeID);
CREATE INDEX IX_Node_SessionId_NodeId ON dbo.Node(SessionId, NodeId);
CREATE INDEX IX_Weight_SessionId_NodeId ON dbo.Weight(SessionId, NodeId);

SELECT TOP(1) *
FROM myTable
WHERE LEGALDESCRIPTION IS NOT NULL
ORDER BY LEGALPARCELID, SEQUENCE_NO

SELECT *
INTO #t
FROM (VALUES
(1001, CONVERT(datetime,'2018-05-26 09:33'), 1),
(1001, '2018-05-26 08:44', 2),
(1002, '2018-05-28 08:22', 1),
(1002, '2018-05-28 12:44', 2),
(1001, '2018-05-21 07:44', 1),

Have you tried using 'nodes'?

;with cteTransfer as
(
  select TOP(1) *
  from #tempOutputTable t
  where t.LogText = 'sUtilFinaliseDB: Transfering Files To Archive Completed'
  order by logdate desc