Convert Color Tiff with single page to grayscale

Hi,
I have an issue in convert color TIF file (single page) to grayscale with JPEG compression and image resolution to be low and image quality to be low with dpi (200,200).
please find the image sample

I’m using the below code, but the out.tif image dimensions are bigger than the original one

from PIL import Image

fil = 'original.tif'
img = Image.open(fil)
rgbimg = Image.new("L", img.size)
rgbimg.paste(img)
rgbimg.save('out.tif', format='JPEG', quality=6,
            dpi=(200, 200), optimize=True)
rgbimg.close()

any help will be appreciated,
thanks.