It's generally a bad sign for a dynasty when rulers stop being given monickers like "The Mighty" or "The Conquerer" and instead wind up with things like "The Drunkard" or "The Bewitched". Once we get down to personal insults then I think we can assume that the writing is on the wall.
Happy birthday then to not one but two Holy Roman Emperors; Charles the Bald and Charles the Fat. Both of them were Holy Roman Emperor during the ninth century and neither of them seemed to enjoy it very much. Charles the Bald, the first out of the gate, was a grandson of the far more impressive Charlemagne (Charles the Great thank you very much) and inherited about a third of the empire his illustrious predecessor had built. Due to the unfortunate Carolingian habit of dividing territory among any sons who hadn't already killed each other Charlemagne's empire didn't last intact for very long. Charles the Bald inherited (after a tedious period of civil wars) the left hand third of the empire, most of which is now France. A period of peace between brothers lasted for the unusually long time of five years. At the end of this time one of his brothers (Louis the German) decided that peace was boring and invaded Charles' kingdom. Charles had meanwhile made himself so unpopular that virtually no-one raised a sword in his defence. Despite kicking Charles around France for a while Louis couldn't persuade the local bishops to crown him king and sloped off back to Germany. This left Charles free to be defeated by rebellious Bretons and then his own nephew.
To make matters worse Vikings were marauding (as Vikings are wont to do) and sacking settlements along the coast. They had a pretty liberal interpretation of the word "coast" and managed to include Paris in the sackings at least once. Charles led armies against them without much success and sent them vast sums of money (slightly more successful although it did tend to tempt the Vikings to come back to see if there was any more).
For some reason this litany of failure made the then pope decide he would be perfect as the new Holy Roman Emperor (the previous one having just died) and Charles went to Italy to gather that kingdom into his domains and be crowned by the pope. While he was away Louis the German who had been an unsuccessful contender for the crown ravaged his lands with fire and sword. When Louis died Charles tried to seize Germany in response and got beaten up again. While licking his wounds he got an urgent email from the pope. The Saracens were attacking and it would be really nice if the Holy Roman Emperor could come and defend Christendom for a while. Charles marched into Italy and absolutely nobody rallied to his standard. Depressed and ill he left for home, dying on the way. The pope who obviously hadn't learnt from experience crowned Charles the Fat as his replacement.
Charles the Fat was a son of Louis the German mentioned above. By comparison with Charles the Bald he was quite the success but only by comparison. His life didn't get off to an auspicious start as he was apparently possessed by a demon. Once that was dealt with (how? Antibiotics?) and perhaps as a reaction he became incredibly religious. He was also the last member of the Carolingian dynasty to rule over the united empire built by Charlemagne. He achieved this by sitting on his backside and waiting for all his other family members to die which they obligingly did.
Meanwhile the pope was having problems. A guy named Guy was encroaching on his territory and the pope dangled the bait of the imperial crown in return for assistance. Charles turned up, got crowned and did nothing to help. The next year he held a conference at which Guy and his father promised to give back the stuff they had pinched from the pope. They didn't.
Peace in Italy thus restored Charles went back to western Europe which was still having Viking problems. Charles gathered a mighty army, surrounded the Viking host and then cut a deal with them. Some time later he had the Viking leader quietly murdered. This solution to the Viking problem proved only temporary and a few years later they were back besieging Paris again. Again Charles raised an army, marched on the Vikings and this time paid them to beat up his own subjects who were in revolt. One can't imagine why.
With whatever reputation he had trashed with this deal he settled down to organise the succession. He had no legitimate heirs so he tried to legitimise his bastard. Unfortunately the bishops were having none of it and the pope (whom Charles hoped would back him up) died inconveniently. Tossing the entire plan out the window Charles called a major conference to decide the succession once and for all. He needn't have bothered, one of his nephews was deciding the succession all by himself. He marched on Germany with an army and it turned out that no-one was sufficiently invested in Charles' continued reign to oppose him. Charles was deposed (quite possibly with a sense of relief by this stage) and died in retirement a few years later. The Carolingian empire fell apart never to be restored although the title of Holy Roman Emperor proved surprisingly durable for an honour that brought nothing but political complications, unsuccessful campaigns in Italy and interaction with a pack of ruthless, grasping political opportunists (I'm talking about the popes).
As far as we can tell Charles the Bald wasn't bald and we have no knowledge of the physical dimensions of Charles the Fat. It is entirely possible that they got these epithets because Charles the Useless and Charles the Twit were considered just a little too blatantly disrespectful for holders of the imperial dignity.