I answered a question the other day about How an English prince ended up with a claim on Sicily, and the background to that actually answers your question:

Sicily in the twelfth century included both the island itself and most of the southern half of the Italian peninsula, with the Papal States bordering it to the north. The Kingdom of the Two Sicilies was basically the same territory but that was a much later kingdom in the 19th century.

In 1154, King Roger II of Sicily died and was succeeded by his eldest surviving son, William I. Roger II had other sons who died before him, including one also named Roger (who died in 1148) - this Roger had an illegitimate son named Tancred. Roger II also left behind a pregnant wife, and his posthumous daughter, Constance, was born later in 1154. William I died in 1166 and was succeeded by his son William II, who ruled until 1189.

William II didn’t have any children, so Constance was his closest legitimate heir. She had married the Holy Roman Emperor, Henry VI, a few years earlier in 1186. The nobility of Sicily, and the Pope, were worried about the imbalance of power if the Emperor also inherited the Kingdom of Sicily. So in 1189 the kingdom was seized by Tancred.

Tancred died in 1194 and was succeeded by his son, William III, who was still a child. He was easily overthrown by Constance a few months later. At the end of 1194, Constance gave birth to her son Frederick.

Emperor Henry died in 1197 when Frederick was only 3. Once again neither the Sicilian nor German nobles, nor the Pope, wanted the same person to control both the Empire and Sicily, so Constance was forced to give up Frederick’s claim to the Empire. Constance also died the next year in 1198. Frederick was now an orphan, and under the protection of Pope Innocent III, who claimed Sicily as a “papal fief” (i.e. a separate, independent kingdom, but also under Innocent’s protection).

So in 1204 Frederick was 10 years old and the king of Sicily, although still a ward of the pope. He had a claim on the Holy Roman Empire through his father, but in order to be emperor he would have to be elected as King of the Germans by the German nobles and then crowned as emperor by the Pope. But in 1204 no one had been crowned emperor since Henry VI died. There were two rival claimants to the Kingdom of Germany, Otto IV and Philip of Swabia. Otto IV eventually won and was crowned emperor in 1209. But he had nothing to do with Sicily. Otto was overthrown in 1215 and for a few years there was no emperor again, until Frederick was finally elected King of Germany and crowned emperor in 1220.

Technically Sicily and the HRE were never legally united - they were two completely separate monarchies, and Frederick just happened to rule both of them. But in practise, having access to the resources of both Sicily and the Empire, and surrounding the Papal States from the north and from the south, made Frederick extremely powerful; too powerful as far as the pope was concerned, and Frederick was overthrown as emperor in 1245. He remained King of Sicily though because the Pope had no authority to depose the king (although after Frederick died in 1250, the pope certainly did claim that authority as well).

Sources:

Rebecca Rist, The Papacy and Crusading in Europe, 1198-1245 (Bloomsbury, 2011)

Alfred Haverkamp, Medieval Germany 1056-1273 (Oxford University Press, 1992)

David Abulafia, Frederick II: A Medieval Emperor (Oxford University Press, 1992)