I don't know how to do that for edges, but here is how you can do it for vertex size:
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In the Excel ribbon, go to NodeXL, Analysis, Graph Metrics.
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In the Graph Metrics dialog box, check "Vertex degree" and click "Calculate". (I'm assuming that your graph is undirected. You can adjust this procedure if it's actually directed. The graph's directedness is set via NodeXL, Graph, Type.) This adds a "Degree" column to the Vertices worksheet.
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Go to NodeXL, Visual Properties, Autofill Columns.
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In the Autofill Columns dialog box, select the Vertices tab.
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On the Vertices tab, set the "source column" for "Vertex Size" to "Degree" and click Autofill. This fills in the "Size" column on the Vertices worksheet with sizes that are proportional to the "Degree" values.
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Show your graph. The size of each vertex in the graph pane will be proportional to the vertex's degree.