PDF files size increasing in printer spooler

One thing to check first. From the print dialog, go to the Advanced options and make sure that the Print as image option is not selected. That option, typically used only to get around serious printer driver problems, forces conversion of all contents in the PDF file to large, high resolution, raster graphics images. If that option is selected, deselect the option and see if that resolves the problem.

Assuming that you weren't using the Print as imge option …

There is only a loose connection between the size of a PDF file and the size of the spool file. What is more germaine are two factors: (1) the nature of the contents of the PDF file and (2) what PDL (Page Description Language) is supported by the printer.

In the first case, simple vector and/or text content with no transparency effects typically yield the smallest spool files. Depending upon the form of compression supported by the target printer (and driver), raster images that are highly compressed in the PDF file may explode in size for the spool file. Any significant amount of transparency effects in the PDF file (including drop shadows, reflections, etc.) result in transparency flattening in the output (with only one major exception). Such transparency flattening can also tremendously balloon the size of the spool file compared to the size of the original PDF file.

The second case is related to what your printer supports as its native PDL (Page Description Language). If the device natively supports PDF and has a proper print driver that alerts Acrobat or Reader of this, the spool file may in fact be very close in size to the original PDF file (I doubt that is the case of low-cost Brother printers). If the printer supports PostScript language level 3 and uses the Windows PSCRIPT5.DLL Type 3 printer driver, unless there is live transparency in your PDF file, the spool file should be fairly reasonable in size (in the case of live transparency, transparency flattening on a particular page can cause the generated PostScript for that page to balloon significantly). For any other PDLs, depending upon what the printer driver needs to convert the PDF content into (for example, does the printer's PDL directly support fonts, complex polygons, etc.), much of the PDF content may actually be converted by the print driver into raster graphics for the spool file. 

If you still have issues around a particular PDF file and its spool file size, post a link to a sample of such a file and we can examine it and see what's going on.