Such a lawsuit is known as a strategic lawsuit against public participation, or SLAPP. In the United States, several states have enacted laws that penalize those whose file SLAPPs. The provisions of these laws vary from state to state, but they usually allow a defendant to file a motion to dismiss on the grounds that their statements were constitutionally protected free speech about a public figure. These laws may allow discovery to be halted until the motion to dismiss is decided; they may also require a plaintiff who files a SLAPP to reimburse the defendant's attorney's fees, possibly also with punitive damages. Some state's laws require the speech to be before a government forum (as opposed to, say, on Twitter), or to be aimed at procuring government action. And several states have no such laws at all.
A summary of various US states' anti-SLAPP laws can be found on the website of the Public Participation Project, an organization advocating the establishment of such laws.
Note that these motions to dismiss are not always brought by "the little guy" against "the big guy". A notable recent case was Stormy Daniels's libel suit against Donald Trump, which was dismissed earlier this year. Daniels had filed suit against Trump claiming that one of Trump's tweets about her was defamatory. Trump moved to dismiss under Texas's anti-SLAPP law, on the grounds that his tweet was protected political speech about a public figure (namely Daniels); and the judge agreed.