Might be good to investigate the structure (or lack thereof) that the screws are going into. Possibly you would be able to reinforce it with e.g. some aluminum plate or extrusions...or possibly make an unwelcome discovery that there is water or other damage there that needs repair.
A somewhat larger diameter screw, by itself, isn't going to have vastly more holding power if it's going into the same luan that the original screws pulled out. It would probably have a little more, but not a lot. Hopefully the screws are actually attaching to some semi-substantial framework.