I was very unwilling to enter into it, as you may imagine, without the knowledge and approbation of his mother; but I was too young and loved him too well to be so prudent as I ought to have been
Approbation means the "action of expressing oneself pleased or satisfied with anything; or the mere feeling of such satisfaction; approval expressed or entertained" (OED).
According to the customs of the time, parents were to be consulted about a marriage and their opinion to be taken in high regard; however, men and women were mostly free to choose their marriage partner. If a young adult did choose someone who their parents disliked, they might be left out of the will or, if they are underaged, they may have permission withheld from them. Parental opinions were often respected by young people. ( Elizabeth Maurer, "Courtship and Marriage in the Eighteenth Century", Web.)