indulgent

Definitions:

Yielding to the wishes of those under us; compliant; not severe.
- Nuttall's Standard dictionary of the English language. By Nuttall, P.Austin. Published 1914. (adjective) (adj.) (adjective)
Compliant; unduly favourable; yielding to the wishes and desires, & c., of those under one's care.
- Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874. (adjective) (adj.) (adjective)
Yielding; compliant; not severe.
- The Clarendon dictionary. By William Hand Browne, Samuel Stehman Haldeman. Published 1894. (adjective) (adj.) (adjective)
Yielding to the wishes of others: compliant: not severe.
- The american dictionary of the english language. By Daniel Lyons. Published 1899. (adjective) (adj.) (adjective)
Yielding to the humor, wishes, etc., of another; showing favor; kind.
- The Winston Simplified Dictionary. By William Dodge Lewis, Edgar Arthur Singer. Published 1919. (adjective) (adj.) (adjective)
Indulgently.
- The Winston Simplified Dictionary. By William Dodge Lewis, Edgar Arthur Singer. Published 1919. (adverb) (adv.) (adverb)

Usage examples:

Mr. Marsh is rather too stout for his years, and I should think very self- indulgent whenever his wife looks at him, he unconsciously falls into the attitude of one who is accustomed to snuff incense.
- The Emancipated by George Gissing
Mr. Dorsett smiles indulgent
- Torchy, Private Sec. by Sewell Ford
Yet it was when they ceased to be strangers that their influence would really be strongest; and so there was good reason, both for the sake of the family they might win, and for themselves who should not become self- indulgent why they should not go from house to house.
- The Gospel According to St. Mark by G. A. Chadwick