I just noticed that the splitting of document pages dramatically increases the document size.

Just to give an example: a pdf document of 385 KB by simple page splitting turns into a document of 1,2 MB. In other words: the splitting trebles its size.

Why is this? And is there something that can be done about it?

There are two reasons for the size increase.
1. Splitting a page creates two copies of that page, so it will double the size of the file.
2. Passing any PDF document through Quartz (the system that processes the PDFs for PDFClerk) can have an effect on the size of the document (making larger or smaller), regardless of splitting.

Neither of these factors is something you or I can do something about unfortunately.

You could specify a reduce file size filter when exporting to PDF, but that is likely not to help much, since it really only reduces the size (and quality) of graphics, if any.

Thanks for your quick answer, António!