I have never heard of a "heavy" tapered barrel. When first introduced in 1970, the Model 64 included a standard tapered barrel (same profile as the Model 10-5 tapered barrel). The 4 inch Model 64s introduced a standard "heavy" barrel in 1972 (similar to the Model 10-6 barrel). The 4 inch tapered barrel was discontinued in 1973.

The 4 inch tapered barrel Model 64s are desirable and are becoming collectible.

Hope this helps.

Steve