I'm American, have lived in many parts of the US, and I agree: "six pound five" is not something that we say. As Gormo says, this construction is frequent for feet and inches ("six foot five"), but would not be standard for weight.
And personally, if I were to use this nonstandard construction, I'd probably pluralize "pounds". I don't know why "foot" is usually singular in the parallel construction.
The most charitable interpretation I can come up with is that your relatives are from the American South, and are actually saying "six point five", meaning 6 and half pounds, and you are mishearing them.
