In Finder, the file size is dimmed I copied a file from my Mac to a server on my LAN. In the Finder window for the destination, the filesize is slightly smaller, and is dimmed.

What does it mean that the filesize is dimmed?

In the screen shot, the file is 1Password.agilekeychain and the size 11.6MB you can see as dimmed. The size on my Mac is 12.2MB.
Dimmed means it is displaying a cached value while waiting for the size to be calculated again.

The .agilekeychain file is in fact a folder with lots of small files in it so it will take a few seconds to finish adding each individual size. Why isn't it there already? Maybe the Finder is occupied calculating another size on a previously opened window, it is not very efficient on focusing its work on the front window. Or the server does something else at this time, for example my Time Capsule can be horrifyingly slow to display folder sizes while indexing a backup.

As for the size difference, it means it has taken its snapshot value at a bad time during the copy process, when the folder was not fully copied. Dimmed values can be unreliable, it's outdated data by definition.

So either you wait for the Finder to update its data and display a correct size (in black), either you open a Terminal window, type du -s --block-size=1000 --apparent-size  [space] then drag and drop your file, you will get its size far quicker (in kiB). Far quicker also because the Finder, in my experience, sometimes "forget" old tasks and never actually update the size :(