There seems to be a sweet spot that nobody pulled off during wartime for purpose-built 'light interceptors', the Caudron and the CW 21 were both failed efforts basically. But there were several other examples that kind of fit into that niche and were quite successful. Lets not forget, the Mosquito was designed to be a 'lightweight' bomber made of wood to save on strategic materials like duralumin which worked out fantastically as both a bomber and a fighter (and a recon, maritime patrol, intruder, and in many other roles). Many of the Soviet fighters were basically made along these same lines (lightweight due to relatively weak engines, using wood to save on aluminum and other strategic materials) and while they really struggled on both the design and (particularly) manufacturing level in the early war, the Yak series certainly turned out to be quite successful by the end, in fact the lightest (I think ?) version, the Yak 3, was widely considered one of the best fighters of the war, though at roughly 5,000 lbs they are on the limit of what would be considered a lightweight fighter by early war standards, by the later war they certainly were (compare to a P-51).
But in terms of weight you can get a lot closer to those two famous designs and find some successful examples. I think you could make a case for some of the biplanes like the Gladiator, I-153 and CR 42 being held over for production, (as well as the monoplane I-16) as being at least somewhat effective 'light fighters' - the Gladiator in particular worked both for point defense (as in Malta) and as a carrier aircraft. In the Pacific you have the Ki-27 "Nate" and the A5M4 which are actually lighter weight than the aforementioned 'light fighters' and were really quite successful, and helpful to have in the inventory, at least for a while. The Ki-27 in particular proved quite deadly against Allied aircraft, it wasn't until P-40s showed up that they started taking unacceptably heavy losses, but they were still being used here and there into 1944. Same could be said for the CR 42 and even the CR 32 in the early days of the fighting in North Africa and elsewhere around the Med. They did some effective work with those fighters.
There was another niche for obsolescent but lightweight aircraft being held over for mainly point defense and sometimes CAS duties, and these include the I-153 and I-16 which were both notoriously outgunned in Russia but as has been pointed out, they did still have some value. The Curtiss Hawk family of fighters was used with some success in places like India and Burma, until quite late in the war. The Axis made similar use of the French D.520 fighter, the Italians and Bulgarians both made some effective use of it mainly for point defense - the Bulgarian D.520 pilots even claimed some B-24s and a couple of P-38s during raids in 1943 and 1944. Compared to a P-38 a D.520 does qualify as a light point defense fighter I'd say. They seemed pretty effective until the bomber raids were escorted by P-51s. Another kind of similar example to the D.520 is the Romanian IAR.80, a nice looking low-wing monoplane developed via circuitous paths from the Polish P.11. They had some success as point defense fighters in raids by B-24s and P-38s, claiming several victories and helping to smash up a couple of those ill-fated Ploesti missions.
Finally there are also the float plane fighters, which act as tertiary battle area point defense fighters, a good example being the F1M 'Pete' which played a useful role in a few engagements, in spite of it's short range. It was basically a point defense against recon planes and unescorted bombers.
Most of these couldn't quite compete against the top level enemy fighter opposition, but as we know in many battle areas of the war either due to range or limited numbers, those were not always available. In those kind of remote or tertiary / secondary battlefield areas a light fighter did seem pretty viable, and some like the Ki-27 punched far above their weight I'd say. Even the Ki-43 qualified as a 'light fighter' by European or American standards, and yet look how many Allied planes they shot down with it. In modern times, sometimes the 'interim' or 'light' fighter designs work out to be fantastic successes compared to a lot of heavier boondogles which never worked out but racked up design and production costs to a dangerous extent. Aside from the wildly successful F-16 (compare that to say, the F-111) I think you could point to the A-4 Skyhawk perhaps, and maybe the MiG -21 and Mirage III, though I admit I don't know enough about the latter two systems design history to say for sure if they merit the category.
CW 21 Empty weight: 3,382 lb (1,534 kg)
Caudron Empty weight: 3,075 lb (1,395 kg)
Ki-27 Empty weight: 2,447 lb (1,110 kg)
A5M4 Empty weight: 2,681 lb (1,216 kg)
Gladiator Empty weight: 3,217 lb (1,459 kg)
I-153 Empty weight: 3,201 lb (1,452 kg)
I-16 Empty weight: 3,285 lb (1,490 kg)
CR 32 Empty weight: 3,208 lb (1,455 kg)
CR 42 Empty weight: 3,929 lb (1,782 kg)
Ki-43 Empty weight: 4,211 lb (1,910 kg)
F1M Empty weight: 4,251 lb (1,928 kg)
P-36 Empty weight: 4,567 lb (2,072 kg)
D.520 Empty weight: 4,680 lb (2,123 kg)
IAR.80 Empty weight: 4,850 lb (2,200 kg)