If you have added a Bevel Weight use Shift G > Bevel (or Selection Menu > Select Similar > Bevel). Super important: This is only visible if you are in edge select mode. Vertex and Face selection modes have different options in that menu.
Have a look at Forgotten Tools. It can save not just vertex groups, but edge and face groups as well. Check it out in this b.a. thread. $5 from the Gumroad link or free from the link below. Sadly - Blender modifiers do not see these selections. But they are still useful.
Do you need to watch a few selection tutorials? You have ways to select that are faster than clicking each edge.
Like this…
Alt-Ctrl Click an edge to select a loop of edges. Shift-Alt-Ctrl Click to deselect the edges between two loops.
Alt Click to select an edge loop.
Select one edge then Ctrl Click another edge to select a line of edges between them. Keep Ctrl clicking to grow the selection.
Selection Menu > Select Sharp Edges almost always selects the correct edges for beveling.
And just in case you do not know about it… The Bevel Weight Setter
You can actually go along an edge loop and add varying weight to the edge. This is one way to get falloff in corners.
Or select vertices in edit mode, then in Weight Paint Mode click the Vertex Icon just to the right of the menu where you go into Weight Paint mode. Then use the Weight Paint gradient tool to paint the weights onto the selected edges…
And with all that… Sometimes you just need to add an extra loop between the loops you want to add bevel weight to, to stop the connecting edges being auto selected. 
Happy edge smoothing…