As shown by the comment and the answer above, I think we can define a rule for the alternate use of "estar" and "tener" when predicating a state about the subject:
"tener" will be used with an abstract noun as direct object or as the magnitude (whether implicitly or explicitly stated) to which a certain measurement or dimension refers.
"estar" will be used with adjectives.
We thus have, apart from the examples with "interés" (noun) and "interesado" (adjective) above, the following:
Estoy hambriento. (adjective)
Tengo hambre. (noun)
Estoy confiado. (adjective)
Tengo confianza. (noun)
Estoy cansado/somnoliento. (adjectives)
Tengo cansancio/sueño. (nouns)
Whenever magnitudes, such as age, height, weight, width, depth, etc., are involved, we can use the verb "tener" or a more specific verb peculiar to the magnitude involved:
- Tengo 50 años (de edad).
- Mide 5 metros (de ancho/alto/profundidad). (I'd say "ancho" and "alto" are nominalized adjectives here.)
- Pesa 100 Kg.
Notice that "estar" and even "ser" will appear whenever there are adjectives in the vicinity.
- El niño es cinco años mayor (older, adjective) que su hermana.
BUT
BUT
- La niña pesa 10 Kg. más de lo que correspondería (tiene 10 Kg. más que el peso que correspondería).
Note: This pattern where "idiomatic tener" is followed by a noun may not appear in grammar books for native speakers, who take it for granted, but is provided as a rule in books for speakers of other languages, as shown below:
In Spanish, "ser" and "estar" will appear with adjectives (or prepositional phrases) respectively denoting permanent or temporary states:
- estar acalorado / con calor ("caliente" may be used to indicate sexual excitement or anger)
- ser cuidadoso
- ser exitoso
- estar con frío
- estar hambriento / con hambre
- estar temeroso / con miedo
- estar en lo cierto
- estar sediento / con sed
- estar somnoliento / con sueño
- ser afortunado/una persona de suerte / estar con suerte