I often find myself moving a window to the side of a monitor. When it does so, it resizes the window, which means I then have to drag the windows edge to increase the size of the window. Is there an option to have it move the window to the size but not resize?

Which version of Windows are you using?
One of the functions within Windows settings allows you to turn of the window resize.
With Windows 10 Open the Settings app, click on System then on Multitasking and you will see the setting you want (its the second one down).

I have two machines, both with dual monitors. The first is a 64-bit Windows 10 machine, the other a 32-bit Windows 7. The behavior I described occurs on both machines.

Pursuant to you suggestion,on the Windows 10 machine I turned OFF the option to automatically size when snapping. However, that did not stop the resizing. Then, just to make sure, I rebooted the system, checked if the option was still set to OFF (it was), and then moved a window to either side on both monitors. Unfortunately, in all cases, the window was resized to a smaller width.

In the same place, turn off the top option: "Arrange windows automatically by dragging them.........."

That stops the aero snap on my machines.