Abarim Publications' online Biblical Greek Dictionary
The curious noun κραββατος (krabbatos) describes a mat or make-shift mattress, apparently made from twigs and leaves, since it stems from the Macedonian word γραβος (grabos), meaning oak. This same Macedonian word also became the Greek noun γραβιον (grabion), which describes a torch made from a bundle of twigs. Where the Macedonians got this word from isn't clear, but it appears to be not Indo-European, or so say the experts.
Here at Abarim Publications we are of course shamelessly biased, but since everybody is guessing, here's our two cents worth: The Macedonian word is spelled with a single b but the Greek one has a double one. That draws our attention to the Hebrew verb רבב (rabab), which speaks of being much or many, and especially many becoming one (many arrows, many rain drops, many instructions, many branches), which would perfectly describe our bundle or twigs. The leading k can then be explained from the common Hebrew prefix כ (ke), meaning like. In Deuteronomy 32:2, Psalm 72:6 and Micah 5:7 appears the term כרביבים (krabybim), meaning "like showers" (literally: like the many).
Part of the pun would be that the familiar noun ραββι (rabbi), meaning rabbi, derives from this verb רבב (rabab), which suggests that the New Testament's familiar image of the paralyzed man upon his κραββατος (krabbatos) may be considered to represent the common Jewish population that's kept lame upon its debilitating rabbinical tradition (see Deuteronomy 21:22-23 and compare Matthew 23:23 to Matthew 13:32). Also note that the name of the feast of Pesah (Passover), namely פסח (pesah), closely relates to the adjective פסח (piseah), lame or cripple.
But whatever its pedigree, our noun κραββατος (krabbatos) is used 12 times in the New Testament; see full concordance. Another word for bed, and describing a proper bed rather than a bundle of twigs, is κλινη (kline) and its diminutive κλινιδιον (klinidion), literally meaning recliner.