Old, but very huge complex web site in Dreamweaver CC, able to see with Big Sur and new dreamweaver?

Dreamweaver CC 2021 is indeed compatible with Big Sur OS. 

Whether or not your site works in modern browsers & mobile devices depends on the code, not the code editor.

Hi @Lou5EC0,

Which version of DW do you have currently?

Creative Suite and earlier are NOT compatible with 64-bit Catalina or Big Sur. 

Worshipers of Saint Steve of Cupertino have long been lamenting about the lack of backwards compatibility.  Meanwhile, Brother Bill of Redmond followers are still blissfully using old software.  🙂

Unfortunately, old Adobe software (pre-Creative Cloud) is no longer available.

So if you upgrade your computer, you'll need to get modern software that's compatible with it.  Or else keep your old computer the same and never, ever upgrade it again.

MODERN CODE EDITORS:
-- Adobe Dreamweaver CC - https://www.adobe.com/products/dreamweaver.html
-- Atom (free) - https://atom.io/
-- Codespaces (free, browser-based) - https://github.com/features/codespaces
-- Nova (Mac only, formerly called Coda) - https://nova.app/
-- Pinegrow - https://pinegrow.com/
-- Sublime Text - http://www.sublimetext.com/
-- Visual Studio Code (free) - https://code.visualstudio.com/
-- Wappler ~ Visual Web App Builder - https://wappler.io/

Hope that helps.