From the description of the spell (emphasis mine):
The weapon can take any shape you choose. Cleric deities associated with a particular weapon (such as St. Cuthbert is known for his mace and Thor for his hammer) Make the effect of this spell look like that weapon.
Unfortunately, Spiritual weapon It only takes the form of a weapon, not its statistics. So the spiritual weapon does not gain attributes like Heavy, Reach, etc. It only looks like any weapon you choose. (Note that the damage dice are also independent of the original weapon).