May be designates a possibility. When written as two separate words, may be is used as a verb. If you can substitute the words could be or might be in your sentence, then you are using may be as a verb and it should be written as two separate words.
Maybe is an adverb which means possibly or perhaps. If you can substitute the word perhaps in your sentence, then you are using maybe as an adverb and it should be written as one word.
Ted Cruz’s book royalties may be higher than Scott Walker’s net worth (The Washington Post)
Indeed, picky eating may be a sign that a young child has psychiatric problems that need to be addressed. (The Los Angeles Times)
Some scientists have speculated the source of extra lithium in young stars may be stellar explosions, or novae, expelling matter into space. (The New York Times)
World’s most intelligent? UK girl achieves highest possible IQ score, may be brainier than Einstein, Hawking (The Indian Express)
Why InMobi may be India’s most innovative company (The Times of India)
Maybe he thinks Prime Minister Narendra Modi, slated to visit Britain in November, will be pleased at his intervention — on the Kohinoor, not on the prime minister’s surnamesake, of course. (The Economic Times)
“Maybe a lifetime’s supply or just the first person to receive a two litre tub, if they do that next,” he said. (The Sydney Morning Herald)
“On a hedged basis, maybe there’s some interest in Aussie bonds, but on an unhedged basis it’s a bit more problematic.” (The Wall Street Journal)