I like fred_dot_u's solution. An additional thought. The pictures look like the front might have a lacquer finish. If so, the heat from soldering might affect it. In that case, you could need to strip the front, polish, and recoat it. It isn't a big deal on something that size, but it would probably remove the patina and leave a polished brass look (although you could restore the patina). Just something to be prepared for if that would make a difference. You could solder the smaller piece first to see how it goes, and have a smaller job if it does create remedial work.
If the front does have a lacquer coating, and you don't want to risk changing the appearance, there's another way to fill the back and add some weight. Get or make fine powder of a heavyish metal (you can use a Dremel tool to grind a scrap piece of steel, copper, or brass), or very fine sand, and build up layers of the powder that you saturate with superglue. If you premix a small amount of baking soda with the powder, the layers will harden quicker. Do it in a well-ventilated place because it produces a lot of fumes.
If you don't want to deal with the fumes or don't have a lot of superglue on-hand, mix the powder with a little glue that will stick to metal to create a clay, and press it into the back to fill it. There's a lot of surface to bind to. Something that thick will take a long time to dry, though.