You can add editors to your site.
While in edit mode click the 'Share with others' icon.
Warning: Revision history is just rolling out to New Sites. If it hasn't been added to your site and an editor makes unwanted changes you can't easily restore the page.
After adding an editor you can transfer ownership to that account. Click the drop-down after the editor's name and change the setting to 'Is owner'. Your owner account will be changed to 'Can edit'. The site files will appear in the new owner's drive. The new owner can remove the original owner or leave him as editor. The only way to get ownership back is for the new owner to make you the owner. Before you transfer ownership you may want to make a copy the site so that you do not lose your work.
In the link sharing window make sure to select "Off - specific people". If you select :On - public on the web" ANYONE will be able to edit your site. See the image at the bottom-left of this page.