Efficient breeding and selection of superior genotypes requires a comprehensive understanding of the genetics of traits. This study was aimed at establishing the general combining ability (GCA), specific combining ability (SCA), and heritability of sweetpotato weevil (Cylas spp.) resistance, storage root yield, and dry matter content in a sweetpotato multi-parental breeding population. A population of 1,896 F1 clones obtained from an 8 × 8 North Carolina II design cross was evaluated with its parents in the field at two sweetpotato weevil hotspots in Uganda, using an augmented row-column design. Clone roots were further evaluated in three rounds of a no-choice feeding laboratory bioassay. Significant GCA effects for parents and SCA effects for families were observed for most traits and all variance components were highly significant (p ≤ 0.001). Narrow-sense heritability estimates for weevil severity, storage root yield, and dry matter content were 0.35, 0.36, and 0.45, respectively. Parental genotypes with superior GCA for weevil resistance included “Mugande,” NASPOT 5, “Dimbuka-bukulula,” and “Wagabolige.” On the other hand, families that displayed the highest levels of resistance to weevils included “Wagabolige” × NASPOT 10 O, NASPOT 5 × “Dimbuka-bukulula,” “Mugande” × “Dimbuka-bukulula,” and NASPOT 11 × NASPOT 7. The moderate levels of narrow-sense heritability observed for the traits, coupled with the significant GCA and SCA effects, suggest that there is potential for their improvement through conventional breeding via hybridization and progeny selection and advancement. Although selection for weevil resistance may, to some extent, be challenging for breeders, efforts could be boosted through applying genomics-assisted breeding. Superior parents and families identified through this study could be deployed in further research involving the genetic improvement of these traits.