The weight value doesn't correspond directly to a p-value. It's either the sum (current & recent CNVkit versions) or mean (some earlier versions) of the weights of the bins that the segment covers. Those weights indicate the estimated standard deviation of bin log2 values in a (possibly hypothetical) pool of normal samples used as the reference -- in the reference .cnn file this is the "spread" column. Reference bins with spread > 1.0 are dropped automatically under the assumption that they're unreliable.

(If your segment weights are all below 1, you might be using an older version of CNVkit. Consider updating to take advantage of recent improvements.)

If you want to quantify the reliability of a segment, try the segmetrics command, in particular the --ci (confidence interval) or --sem (standard error) options.