Couple of doubts: 1) The CLT requires you to have population distribution and population parameters before it can you used. Correct ? It cannot be then used to solve problems where getting an entire population distribution is not feasible. E.g. What is the prob. of having weight of people greater than 160lbs in U.S. We wouldn't know the population weight distribution to begin with. How can this be estimated then ?
2) Given we have a population distribution, the whole point of CLT is to aid in calculating probabilities simpler ?
1) The idea behind the central limit theorem is the following.
Suppose you go out and collect data $X_1, X_2, ...,X_n$ where each $X_{i}$ has a finite mean $\mu$ and variance $\sigma^2$.
Then $\bar{X}$ is distributed as a Normal RV with mean $\mu$ and variance $\sigma^2/n$ as $n \rightarrow \infty$. This is an amazing result. It means, that you can go out, collect data of any type (assuming it satisfies the constant finite mean and variance), and that the average of that data will be Normal.
Usually for practical purposes, n does not have to be very large, 20 or 30 observations is usually enough. Most examples I see are between 30-50 observations.
So in regards to your question, you don't need to know the weight distribution of the population. By the central limit theorem, you know the weight distribution of the average person.
2) If you have a population distribution, you can then use it calculate probabilities of an individual observation. The distribution of the mean of that variable will still be normal by what I describe above.