Quick answer: No, a lighter boat will not make
you go faster. (though for some, it may, see below).
Reasoning: you could put Oscar in a V7 and he would still beat the majority of paddlers. Why? Perfect form, perfect stability, intuitive wave reading, years of experience. The weight of the pro's boats probably only reduces time on a 2 hour race in the order of <1%. Probably less than that, like 0.3%
As you are new and in an tippy boat, you are 1000% more limited by stability and form more than your boat's weight. On the list of "things that make you go faster" the weight of your boat is near the bottom.
The exception may be, a lighter boat accelerates onto a wave easier, so if you are missing waves (but all other things are in sync), a lighter and possibly shorter boat may help with this. However, I do not think this is the case for you, because if you are unstable and miss a paddle stroke, that is preventing you from getting on the wave 100x more than 7 lbs of weight.
I forget if it was oscar or the Mockes who said "if you are bracing more than once every 10 minutes in a downwind you should be in a more stable boat". It sounds like you are still getting the stability down in flat to small conditions, so you have many other things limiting your speed.
A shorter boat has less skin resistance, so if you are not at hull speed (which few people really achieve for any significant period of time), a shorter boat is faster for most people, and its inherently lighter (less material), and it rides short interval waves better (surfs wind waves better), so length is worth looking at and possibly considering a shorter boat.
In general, the V12 is already an elite boat and you will only see
very small speed gains from a newer hull or lighter boat. Stay focused on Stability training and Form. Both of those will pay dividends much faster and much more than 7lbs.
Also, compared to the rest of us, South Africans, Australians, and maybe the kiwi's have a different definition of "stable" and "fast". down there babies are born into Olympic K1's I think. for the rest of us, we just scratch our heads and swim