Objection 1. It would seem that children ought not to suffer any loss through being illegitimate. For a child should not be punished on account of his father's sin, according to the Lord's saying (Ezekiel 18:20). But it is not his own but his father's fault that he is born of an unlawful union. Therefore he should not incur a loss on this account.
Objection 2. Further, human justice is copied from Divine. Now God confers natural goods equally on legitimate and illegitimate children. Therefore illegitimate should be equalled to legitimate children according to human laws.
On the contrary, It is stated (Genesis 25:5-6) that "Abraham gave all his possessions to Isaac, and that to the children of the concubines he gave gifts": and yet the latter were not born of an unlawful intercourse. Much more, therefore, ought those born of an unlawful intercourse to incur loss by not inheriting their father's property.
I answer that, A person is said to incur a loss for some cause in two ways: First, because he is deprived of his due, and thus an illegitimate child incurs no loss. Secondly, because something is not due to him, which might have been due otherwise, and thus an illegitimate son incurs a twofold loss. First because he is excluded from legitimate acts such as offices and dignities, which require a certain respectability in those who perform them. Secondly, he incurs a loss by not succeeding to his father's inheritance. Nevertheless natural sons can inherit a sixth only, whereas spurious children cannot inherit any portion, although by natural law their parents are bound to provide for their needs. Hence it is part of a bishop's care to compel both parents to provide for them.
Reply to Objection 1. To incur a loss in this second way is not a punishment. Hence we do not say that a person is punished by not succeeding to the throne through not being the king's son. In like manner it is no punishment to an illegitimate child that he has no right to that which belongs to the legitimate children.
Reply to Objection 2. Illegitimate intercourse is contrary to the law, not as an act of the generative power, but as proceeding from a wicked will. Hence an illegitimate son incurs a loss, not in those things which come to him by his natural origin, but in those things which are dependent on the will for being done or possessed.
Source: Summa Theologica (New Advent)