I have a list of ages and then a binary value associated with it (e.g. is the person overweight)
I would like to calculate from this the p-value.
I have plotted the values and then calculated the probability that at a certain age the person is overweight, but I don't think this is the p-value.
P-values are used to provide insight into the solidity or likeliness of your results within the framework of a pre-determined hypothesis. Therefore, in order to determine the p-value, first you'll need to identify what you are curious about within the scope of the problem and develop a hypothesis test that mirrors that question.
For example, let's re-frame your data such that we have a clear question that we are trying to answer:
We have a sample of individuals and are given their ages and whether or not they are considered overweight based on their weight being above or below some threshold. Given this data, I would like to know if people who are overweight tend to be of a higher age than people who are not overweight. Given this question, I can then construct the following hypothesis in which $\mu(x)$ is the population mean age of overweight individuals and $\mu(y)$ is the population mean age of non-overweight individuals:
$$H_{0}: \mu_{x} = \mu_{y}$$
$$H_{A}: \mu_{x} > \mu_{y}$$
From there, based on the distribution of your data, you will be able to find the p-value, which is the "probability of observing a result equal or more extreme in your sample, assuming that the null hypothesis is true. If we observe a very small p-value (usually smaller than 0.05), then it is unlikely that our null hypothesis was true. Conversely, with a large p-value, we would "fail to reject" the null hypothesis that the mean ages are equal.
