A standard 4ft chain harrow offer a smooth side and a spiky side. The spiky side can be towed so that the spikes are angled back or forward. When pointing forward, the harrow digs in more and breaks up the soil. Otherwise the harrow is like a rake and mainly levels the soil.
Having said all of that, it depends on the type of soil and whether it is wet (muddy), damp (crumbly) or dry (rock hand or sandy dust) at the time you use the harrow.
I haven't been hugely impressed with my use of the same implement but I took a 4ft length of 3" angle bar, drilled some holes to line up with the hooks on the harrow and hung the bar on the trailing edge. The weight of the bar increases the impact of the harrow by about 50%.
I also have a small (3ft) disk harrow which is heavy and more expensive (£750-ish) and on hard dry ground it also does very little. On damp ground, it breaks up the top inch of the soil and takes out small weeds quite well.
You can also fit a second chain harrow behind the first one to increase its impact but the resulting drag might make your tractor/quad hard to steer. Obviously, you could try with one and get a second if you want to increase the levelling/weeding ability of the harrow.
Sorry if that's a bit of a ramble but I hope it helps
NN