Webers are dual barrel compound carbs, meaning the throttle plates open simultaneously. Solex could probably be a single barrel carb. A more efficient alternative to dual compound carbs would be the dual progressive. In this type of carb, the primary side feeds the engine idle to mid-throttle, and the secondary only begins to open up at mid-throttle.
Putting in a large or high flow carb on an unmodified engine is useless. The engine cannot take in additional charge if it is not capable of expelling an equal extra amount of spent exhaust gases. That is why the logical way of modifying an engine is to first improve the exhaust before upgrading the intake. Besides, a carb's "footprint" must match the intake manifold or else there will be a lot of mismatched surfaces which will lead to gas flow turbulence, not to mention, leaks.
Here's what I suggest:
1. Switch to a freer flowing muffler. Preferrably a nice deep sounding one so that you dont only gain on the reduced backpressure but you also get the additonal attractive exhaust note.
2. Install headers that *perfectly* fit the exhaust ports of your engine. If the holes do not match, take the cylinder head and the headers to the machine shop and have them matched. You can also ask them to polish the ports.
3. Install a freer breathing air filter like the cone types that you see showcased among the tuner crowd. The freer breathing filter should help increase airflow into the carb and engine, making good use of the increased exhaust gas flow.
4. Install a cold air intake. But make sure that the cold air intake will indeed pull in cold air for the carb, otherwise you defeat the purpose. It's best to take the car to the shop for this because you can then ask them to make a airbox that will house the cone type air filter and keep it from inhaling hot air inside the engine. IF your car has 4 headlights, remove one headlight and use the hole to siphon in cold air into the airbox.
OR
4. Have a ram-air intake built on your hood. Make sure it's properly designed so that the scoop feeds the air straight into the air filter. If you can, have the fabricator make a rubber seal around the scoop and the air filter so that all that air gets forced into the air filter and is not wasted into the engine bay.
...that's about it. I wouldnt advice on switching to bigger carbs because I doubt there is an aftermarket performance carb specifically designed for your engine. As I said earlier if the carb is not properly matched for your engine and it's supporting hardware, you just end up wasting money on your investment, plus the engine is now going to be more wasteful, if it's not going to give any performance troubles, such as stumbling from an overrich mixture.