I want to know is marriage with half-cousin's girl more risky than marriage with a non-family girl?
Also I like to know if her parent are cousins(but from mother side), does it add more risk to this marriage or not?
Biology Stack Exchange is a question and answer site for biology researchers, academics, and students. It only takes a minute to sign up.Sign up to join this community
The medical term here is consanguinity, or a consanguineous union. The risks of consanguinity are well studied, and based on the principle that children born to parents with shared genes are more likely to be homozygous for recessive alleles. Population level measurements of specific risks for, e.g., fetal loss, major birth defects, or other problems vary depending on the population studied. Many of these studies look at first cousins, where typical numbers are between a 1-5% greater risk for major birth defects and 4-5% greater risk for late miscarriage or death of a child before age 10. The data on earlier fetal or embryonic loss isn't conclusive. You can read more about this in the review I linked to at the end of this answer. The specific risk for a specific individual isn't on topic here, since it is a personal medical question. If you are looking for an answer to that question, I'd suggest scheduling a visit with a medical geneticist.
Your diagram depicts marriage between half first cousins once removed, with an expected shared percentage of genes of 3.125%, equivalent to second cousins, which fits the definition of consanguinity generally used in the medical literature and allows application of studies that use that definition. The fact that one of the potential parents in this marriage was also the product of a consanguineous union may increase the risk.
Consanguinity is an important risk factor for many birth defects and other diseases (see Cecil Medicine Chapter 41 and this review)