Is a girl's mother entitled to refuse a suitor due to a slight physical difference between them? Does religion prohibit marriage for this reason? And what is the way to convince her?

The mother does not have the right to refuse her daughter's marriage for the reasons you mentioned, as the primary consideration for compatibility between spouses is religiosity. The girl should try to convince her mother and seek help from someone who can persuade her. If the mother insists on refusing and the girl wishes to marry, the mother does not have the right to prevent her, because guardianship in marriage belongs to males, and the father has the most right to it. If the guardian prevents the marriage, it is considered 'adhl (unjust prevention), and the girl has the right to refer her case to a judge. Nevertheless, honoring and being kind to the mother is obligatory in all circumstances.