A scientist found a sample of carbon-14 that weighs \(\frac{2}{3}\) of an ounce. Another scientist found a sample of carbon-14 that weighs \(\frac{4}{3}\) ounces. Suppose they find two additional samples. The first sample weighs \(\frac{9}{16}\) of an ounce. If the scientists assume the ratio of the weights of the first two samples is the same as the ratio of the weights of the last two samples, what does the fourth sample weigh? Provide your answer in simplified form.