It is time to proceed beyond the ancient catalogue of 1999. Welcome to this century. Welcome to the current classification of the Curculionoidea.

 
The erstwhile family "Nanophyidae" has been in disuse for about 20 years. This monophyletic group is rightly the subfamily Nanophyinae of the family Brentidae. This arrangement makes perfect sense upon closer and citical investigation of key morphological features. It has also been recovered as such in a number of molecular phylogenetic analyses. This is also the arrangement now found in catalogues from anywhere in the world, a few of which are listed below.
 
 

For this particular topic I recommend the following introductory reading matter:

(1) Oberprieler RG (2000) The larvae of the weevil tribe Eurhynchini and the phylogeny of the Brentidae (Coleoptera: Curculionoidea). Invertebrate Taxonomy 14(6): 755–770. https://doi.org/10.1071/IT00032.

(2) Bouchard P, Bousquet Y, Davies AE, Alonso-Zarazaga MA, Lawrence JF, Lyal CHC, Newton AF, Reid CAM, Schmitt M, Ślipiński SA, Smith ABT (2011) Family-group names in Coleoptera (Insecta). ZooKeys 88: 1–972. https://dx.doi.org/10.3897%2Fzookeys.88.807. OPEN ACCESS

(3) Oberprieler RG (2014b) 3.6 Brentidae Billberg, 1820. In: Leschen RAB, Beutel RG (eds) Handbook of Zoology. Arthropoda: Insecta. Coleoptera, Beetles. Volume 3: Morphology and Systematics (Phytophaga). Walter de Gruyter, Berlin/Boston. pp. 363–423. https://www.degruyter.com/view/book/9783110274462/10.1515/9783110274462.363.xml.

(4) Pullen KR, Jennings D, Oberprieler RG (2014) Annotated catalogue of Australian weevils (Coleoptera: Curculionoidea). Zootaxa 3896: 1–481. doi:10.11646/zootaxa.3896.1.1. https://doi.org/10.11646/zootaxa.3896.1.1.

(5) Alonso-Zarazaga MA, Barrios H, Borovec R, Bouchard P, Caldara R, Colonnelli E, Gültekin L, Hlaváč P, Korotyaev B, Lyal CHC, Machado A, Meregalli M, Pierotti H, Ren L, Sánchez-Ruiz M, Sforzi A, Silfverberg H, Skuhrovec J, Trýzna M, Velázquez de Castro AJ, Yunakov NN (2017) Cooperative catalogue of Palaearctic Coleoptera Curculionoidea. Monografías Electrónicas SEA 8: 1–729. http://sea-entomologia.org/monoelec.html. OPEN ACCESS