Unknown. Aquilina rejects a derivation from Arabic يَا سَلام (yā salām). The required contraction of sliem into -ssu is indeed unlikely. However, Aquilina’s own connection with Arabic يَسَّ (yassa, “to journey”) seems even less plausible.
The phrase is reminiscent of dialectal Arabic الله عَلَيْك (allāh ʕalayk), which often has the same sense of “bravo!, well done!”. The word jessu would then be Christian Arabic يَسُوع (yasūʕ, “Jesus”). The unexpected gemination is not problematic in this exclamatory context. However, it is questionable whether يَسُوع (yasūʕ) was ever used in Malta. While there were Arabic-speaking missionaries, no Christian Arabic names are found. Moreover, the Islamic name form Għisa is attested (though it is not entirely clear whether the Maltese actually used it among themselves or knew it mainly through Muslim slaves).
jessu għalik!