The theory behind the four smaller front wheels was to increase cornering and braking power and lowering aerodynamic drag. The problem was that the team struggled to get the steering goemetry to perfectly balance, tire scrub in turns led to more energy loss than anticipated, and yes there was the additional weight penalty.
In the second season the P34 raced (1977), the team introduced a lengthened chassis with the front wheels moved further out to improve handling, but that destroyed the aerodynamic benefit of hiding them behind the front spoiler. Supposed;y, the thing that sealed the P34's fate was Goodyear's decision not to continue development of the small front tires.
The Tamiya kits represent the 1976 season cars, plus the carryover chassis raced in 1977. Fujimi makes the 1977 year version, with the slug-shaped upper cowl and extended front wheels. One thing both Tamiya and Fujimi missed was that the 1977 cars had a rectangular tach literally pasted over the original round tach.
A very small omission, but an interesting bit of trivia.