That emotional attachment exists, I made this from scratch, and watched it grow over time.
The site is worth whatever it is worth to the acquirer.
Once you figure out that number, you decide if you want to sell it at that price or not.
Until you get to that point, don't bother thinking about the emotional attachment.
Also, if you get a pile of money, you'll go on and do something fun with it (a whole new project?). You'll establish an emotional attachment to that project too.
It might be worth more to you, but if it is, you simply don't sell it.