Should a young man proceed with marrying a female relative whose husband has died and with whom she had no children, given his fear of regret, or should he back out?

If the woman is as you described—pious, of good character, and beautiful—her being a widow does not diminish her, and you are permitted to propose to her, as long as she has not already agreed to another suitor. If she has agreed to another suitor, then it is not permissible for you to propose to her, due to the Prophet’s (peace and blessings be upon him) saying: “A man should not propose marriage when his brother has already proposed, unless the first suitor gives up, or gives him permission.” However, if there has been no agreement, you may proceed with proposing to her due to her praiseworthy qualities. Although virgins are preferred in marriage, there is no harm in choosing a non-virgin (a woman who has been married before) if she is religious and of good character, especially if there is a benefit, such as the woman having experience or the suitor having children. Compare the benefits and harms, seek guidance from Allah (istikharah), and then rely upon Him.