Being of Irish origin I can surely relate to Dicks being tight as a result of a night on the town. Ever seen them throwing their hats when their horse comes in first past the post?
During a visit to Lexington, MA a few years ago, a guide showing us through the original tavern near the Minuteman statue shared with us his explanation of a number of those "from whence came ....." words. With regards to "sleep TIGHT" he showed us how the beds common to taverns during the 1700s were constructed with suspension systems of ropes. Some of which were tied between the headboard and the footboard while others were tied between the sideboards. At each connection point of rope and board there was a screw threaded tightening mechanism that when tightened taut all around, provided a suspension system with minimum sag in the middle and consequently maximum comfort for the bed's occupant. According to the guide, using the expression "Sleep tight!" was equivalent to saying "Sleep comfortably!".