There are essentially three questions here: why were 2 and 3 Para used to reinforce 3 Commando Brigade rather than more Royal Marines, why 2 and 3 Para rather than another Army unit, and why were they not used as airborne troops?

To answer the easiest question first, more Royal Marine units were not used to reinforce 3 Commando Brigade because they did not exist. The Royal Marines were, and are a small force, and the three Commandos (battalion equivalents) of 3 Cdo Bde represented the entirety of its combat forces. The only significant Royal Marine unit not deployed as part of the Falklands Task Force was the Comacchio Company (later 43 Commando), which was responsible for security at HMNB Clyde (where the British nuclear deterrent was based). It should also be noted that 3 Cdo Bde's supporting units (engineers and artillery) were Army units, rather than Royal Marine ones, further emphasizing the fact that the Royal Marines were a small institution. As such, Army units had to be used to reinforce 3 Cdo Bde.

This then brings up a further question: why the Paras, rather than, say, the Rifle Brigade or any other Army unit? The answer to this lies in the British Army's deployment in 1982. The majority of the Army's regular combat formations were in Germany, as the British Army of the Rhine. Those in the UK were second-line units or Territorial Army formations, with the exception of the Guards Brigade, a more ceremonial formation. The only units that were ready to move at a moment's notice were 3 Cdo Bde and 5 Airborne Brigade, Britain's Quick Reaction Forces. These were the only forces that could be moved to the South Atlantic swiftly enough; however, there was not initially sufficient shipping to move both formations south. As 3 Cdo Bde was the more specialized amphibious formation, and one that was more experienced with mountain and arctic warfare, it was clear that it should be prioritized; however, the two parachute battalions of 5 Airborne Bde could also be carried, and needed to be, as 3 Cdo Bde was not strong enough to face the Argentinian forces on the islands.

So, why were they used as an amphibious, rather than an airborne force? Well, the first difficulty was distance. The nearest RAF base to the islands was Wideawake Field on Ascension Island. This was 3400 nautical miles from the Falklands Islands. The RAF's Hercules C.1 and C.3 aircraft, used for parachute drops, did not have sufficient range to reach the islands from Ascension. They were not, at least initially, fitted with in flight refuelling equipment (though a few would be by the end of the war). This effectively prevented airborne insertion of 2 and 3 Para. However, even if the Falklands had been closer to Ascension, no paradrop would have taken place; the FAA and RAF could not guarantee air superiority over the Falklands, which would be necessary for a paradrop. There were also issues with Argentinian air defenses, especially around Port Stanley.

We can also look at the situation in San Carlos Water on a tactical level, to understand why the commanders made the choices they did. The British had five battalions available to them; 40, 42 and 45 Commandos Royal Marines, and 2 and 3 Para. It was decided to deploy the troops in two waves, with 40 Cdo and 2 Para deploying first, while 3 Para and 45 Cdo deployed in the second. 42 Cdo would remain as an afloat reserve. It made sense to retain an amphibiously focused force as a reserve, as they would need to be capable of responding to any situation that came up. However, it did not make sense to deploy both remaining Commandos in the first wave. To secure the landing sites around San Carlos, and to secure routes further into the interior of East Falkland, the British needed to secure the Sussex Mountains, at the south end of San Carlos Water. The Para battalions, which had an extra company and additional supporting weapons compared to the Marine Commandos, were seen as more capable at holding this vital objective. Using 2 Para to take them would also put the unit closer to its next objective, the airfield and settlement at Goose Green and Darwin. As such, 2 Para formed part of the first wave, and moved immediately to the Sussex mountains.