In the 1920s and 1930s, the US Cavalry was prohibited by statute from using tanks (which were allocated entirely to the US Infantry until the formation of the Armor branch). Attempts were made to skirt this prohibition by the expedient of calling M2 light tanks "combat cars", but these attempts were quashed by Congress after they were discovered in 1935. With the increasing mechanization of the Army, the Cavalry began to replace it's horses with vehicles as well, the first steps being the M2 and M3 scout cars. These vehicles were mechanically reliable enough, but their narrow tires and limited power made them unsuited for off-road use except in good conditions and adding additional weight with the addition of a turret was clearly not going to result in an improvement.
The Cavalry branch decided it needed vehicles for recon that were heavier and better armed and armored than the scout cars, but it was prohibited by statute from owning tanks (the basic definition of which was "an armored vehicle propelled by tracks"). The new armored cars would need to be protected against .30" fire or shell splinters from the sides and .50" fire from the front, it was decided, since they were intended to be recon units not intended to fight heavier vehicles in a toe-to-toe slugging match (note: deck and belly armor were not a priority, open topped turrets were expected to allow better visibility for the crew and light weight was a requirement).
Primary armament-wise, the options were somewhat slim: the .50" HMG was a good weapon, but the scout cars already mounted it. The rest of the weapons in the US Army inventory that might possibly be suitable were the 1.5" AT gun and the (too heavy) 1.5" AA gun, then the new 2" AT gun, the (unsuitable for direct fire) 2.2" light mortar, and the (too heavy) 3" field gun, the (even heavier) 3" AA gun, and the (interesting, but poor trajectory and limited ammunition choices) 3" pack howitzer. In the end, in 1936 the Cavalry chose the 1.5" gun (with a load out of equal numbers of AP, HE, and canister rounds) for the light armored car, and the 2" gun (with a similar loadout of AP, HE, and canister) for the heavy armored car, though the intent was to trial a heavy armored car with the 3" pack howitzer as a possible support car. The mix of ammunition types was intended to give the vehicle commander options when he encountered hostile forces: the AP rounds would allow him to engage light-to-medium armored vehicles, the HE would allow him to engage strong points or soft-skinned vehicles, and the canister would be useful against infantry or guns and their crews at close range.
The Cavalry, having encountered the limits of the M-2 and M-3 scout cars, was also interested in seeing the new armored cars do better off-road than their predecessors, so it required at least the same power-to-weight ratio and a lower ground pressure than the scout cars had.
[Note: in contrast to OTL history, the Cavalry is in charge of the development of US armored cars here in WW, as opposed to essentially being second fiddle behind the Tank Destroyer Corps as it was in OTL (and then the Tank Destroyer Corps pretty much abandoned the M8 after making decisions that made it less capable as a scouting vehicle). As in OTL, in service upgrades to the belly protection on these vehicles is a likely change should they see combat, as is a change from the .30" AA MG to a .50" AA HMG over time.]