To copy a Range of Data to a new sheet, without having to resize all the Column Widths to how you had it in the original, use Paste Special > Column Widths.
There are 2 ways to do this.
Option 1: First Copy, then right click to get your Pop-up Menu. Hover over the Paste Special arrow (>) and click on the Column Widths icon.
Option 2: First do a Normal Copy (ctrl + C) and Paste (Ctrl + V). Then Paste the Column Widths over the top using the Paste Special Dialogue Box. (Ctrl + alt + V, W – to select column Widths and then press enter to select OK). This is a 2-step process but enables you to do it using Keyboard Shortcuts.