Solutions are dictated by goals and budgets, we often compromise one for the other. Since you say you have just a few "carp" in your pond, I am assuming you mean grass carp since common carp would have multiplied many times over to create a population that would threaten the health of your pond.
Decide between your priorities here...
1) good fishing / big fish
3)manageable levels of weeds
4)all of the above
Adding a few more grass carp will control the weeds for a while. Over time you will end up with either too many carp which results in murky water , or too few which is your scenario with too many weeds. They tend to one end of the spectrum or the other with a period of time that is within the range of desirability. The fishing is good for while, then declines depending on the amount of weeds and phytoplankton available. This process is an endless cycle of good and bad.
The next least expensive technique is to actually fertilize the pond and run an aerator to produce heavy phytoplankton blooms. You get bigger warm water fish (not trout) and the algae keeps the rooted plants from growing. This is a more stable or predictable method as long as green water is fine with you. The fishing will be better too.
If you really want to have it all: big fish, clear water and just the right amount of vegetation and the ultimate property value in a habitat that will persist for centuries, this is where we come in. We rebuild these habitats to become the "perfect beast". It's not cheap; it is the ultimate value.
While I rarely comment on techniques recommended on internet sites (because you just cannot keep up with all the bad advice on these sites), I will comment in this case. Liming a pond is like using slow speed dynamite. It's a great tool in the right hands. The intermediate effects vary widely depending on water chemistry and condition of the watershed. If used too much, it will eventually ruin a fishery and cause chronic weed growth of weed varieties that grass carp do not prefer. We are actually working on rehabilitating one of these scenarios this week. Just remember what seems to work in one case for a while, will not work everywhere. We use techniques that work over the long-term and not those which contribute to long-term problems.
I believe it was that great American Philosopher, Popeye who said "ya payz yer money and ya takes yer chances". That pretty much sums up lake and pond management.
A big thing to keep in mind is our pond is natural spring fed The water naturally changes itself at a pretty fair rate. When I bought our carp I was told they were sterile so they will not multiply. We have only "seen" em once since we added em and that was near the pier feeding. Our water quality seems fine and we have visability to about 5 ft on a sunny day maybe a bit more with polarized glasses. There is a great deal of algea growing in our pond as well. No problems with the fishing and no dynamite so far.
The above suggestions are sound advice and you should seek the help of a proffesional like the man above. I was simply stating what we do as we were asked. Our pond requires lime added so we add it. The water is fine and constantly filtered thru the natural spring.