He was prosecuted on ZERO evidence if one discounts the perjury of Jefferson’s cronies.
And that's a pretty big IF. Wilkinson wasn't simply a nobody off the street. He was a high ranking general and territorial governor. He was also, it turns out, a scoundrel, but an allegation of the type he made from a person of his rank cannot simply be brushed aside and ignored. Furthermore, while Burr was likely not guilty of the exaggerated charges of "invasion" that Wilkinson levied against him, it is indisputable that he was up to something no good. In short, a trial of some sort was practically inevitable and to fault it for even happening at all, as you seem to do, betrays more of your own personal animosity against Jefferson than anything of that trial's particulars, or Marshall's conduct in it.
Jefferson (and almost everyone else) knew that Wilkinson was a crook and he had in a cabinet meeting discussed dismissing him from command a few years before because of his corruption. Wilkinson had been in the pay of the Spanish for years and it was no secret.
Jefferson’s true character was shown by this trial by his acquiescence in Wilkinson’s disregard of and wholesale violation of the law and the fact that it became evident that W. had been a bigger mover in any plot than Burr.
I have no problem with a trial but a BIG problem with total disregard of the law Jefferson condoned as well as his attempt to convict Burr prior to the trial in the press by pronouncements about his certain guilt.
There is ZERO evidence that Burr had any intention of splitting the western states from the Union in this case. All evidence pointed to confirmation of his claim that he was aiming to settle lands in the Bastrop tract (area around present day Monroe, La. and to be prepared for war with Spain wherein he would seize Mexico. At that time war with Spain was widely expected even by Jefferson, the ultra-pacifist.
Rather than foiling any treasonous plot Jefferson’s intent ONLY was to destroy Burr now his greatest enemy after Hamilton’s murder. In his mind only Burr stood between the Virginia dynasty and decades of power. He had to be destroyed by any means fair or foul.