Many theories proposed in the comments section below.. Here is my take on a possible explanation. It is expected that a woman's ability to retain her husband and create a happy home is positively correlated to her attractiveness [Note that I am not saying that this is the only factor]. Males are more ready to leave their spouses if they are not attractive, e.g., if they find, or hope to find, another woman that is more attractive. If they decide to stay in the marriage, then the knowledge that their wives are unattractive, and especially the comparison with other women (of one's friends or celebrities) will be a constant source of disappointment, leading to marital friction. Hence, daughters in homes with absent fathers or unhappy homes are less attractive because their mothers are less attractive.
I should say that the authors do propose alternative explanations in their paper, although their data cannot be used to differentiate between them:
It is important to note that this study cannot distinguish between the possible environmental and hereditary influences underlying the relationships between family background and physical development. There are several ways in which health of offspring might be linked to parental relationship. Family stress may negatively impact on offspring health via the immunosuppressant effects of cortisol or high-stress families may have less healthy lifestyles. Alternatively, heritable parental health may influence both offspring health and parental marital relations. Finally, less healthy children may be a catalyst for difficult relationships between parents.Proceedings of The Royal Society B
ISSN: 0962-8452 (Paper) 1471-2954 (Online)
Facial and bodily correlates of family background
Lynda G. Boothroyd et al.
It has been suggested that absence of the father during early childhood has long-reaching effects on reproductive strategy and development of offspring. This paper reports two studies designed to investigate the physical characteristics of daughters associated with father absence. Study 1 used a facial averaging method to produce composite images of faces of women whose parents separated during their childhood (who were 'father absent'), women whose parents remained together, but had poor quality relationships and women whose parents were together and had good quality relationships. Images were then rated by male and female judges. Father absence and poor parental relationships were associated with apparent facial masculinity and reduced attractiveness in daughters. Poor parental relationships were also associated with reduced apparent health. Study 2 compared family background with body measurements and found that father absence or a poor quality relationship between parents were associated with body masculinity (high waist-to-hip ratio) and increased weight-for-height and adiposity. These results highlight the possibility of physical masculinization being associated with purported father absence 'effects'.