Which carmaker's stock has risen the most — some fivefold — since the beginning of 2012, besides Tesla Motors Inc.? Subaru producer Fuji Heavy Industries Ltd.

Profits and sales are heading toward record levels as Fuji Heavy benefits more than most other Japanese automakers from the yen's weakening and as new models such as the BRZ sports car have grown so popular that U.S. consumers have to wait months to buy one.

The success is leading Fuji Heavy President Yasuyuki Yoshinaga to worry whether Subaru, the niche maker of all-wheel-drive vehicles, is getting too big.