My answer is taken from some comments I made in another threadanother thread, and is a continuation of Avek's answer aboveAvek's answer above. Ontop of what Avek stated, and Null makes a reference to itmakes a reference to it, another motivation may be considered as well: The Empire would be highly motivated to cover up their ongoing search for the missing Death Star plans.
As Avek mentions, covering up the arrest of Leia is useful:
to prevent outrage and more sympathy for the Rebellion is correct
they want to question Leia in secrecy about the plans and the secret Rebel base
It is also reasonable that they want to cover up the second half of the operation on Tatooine to be comprehensive about it. Killing the Jawas draws attention, even though Tatooine is a remote planet and the Empire control the Holonet news. If anyone found out about Leia's arrest, the killing of the Jawas in proximity of time and place could draw extra attention.
However, a counterpoint could be that Leia's movements were not secret (she claimed to be on a diplomatic mission to Alderaan), so even if anyone found out about her arrest, it isn't certain that they would make a connection between Leia being arrested near a Tatooine, and a bunch of Jawas being slaughtered there later on by Imperial Stormtroopers. They might, which is why the Empire would want it hushed up if anyone found out about Leia's arrest, and they certainly wouldn't want people digging around, which is the point that Avek makes.
However, this motivation is particularly meaningful when you consider that the one group of people who the Empire absolutely do not want to know about it is the one group of people that information would be meaningful towards: members of the Rebellion.
In Legends, Vader is aware that Leia has the plans and is carrying them to another location (mentioned indirectly in the Note section of my answere herehere). When she ditches them she knows she will be captured so she can't retrieve them, the inference being that someone else can/will, someone else who can investigate the crashed pod the same way the Stormtroopers did. Presumably the Empire doesn't want those people knowing that it is on their trail and going after the plans, especially if they are not yet aware that Leia has been intercepted. The Empire can't know that Tatooine wasn't the intended dropoff point for them.