Exceptionally means to an unusually great degree. Exceptionally good, exceptionally cold, exceptionally well.
It is a strong intensifier and it keeps a trace of its literal sense — an exceptionally cold winter is one that stands outside the usual range, which is why it sits well with measured things. It also means by way of exception: exceptionally, the rule may be waived. Note exception, exceptional.
1adverbexceptionallyTo an unusually great degree.
“The weather was exceptionally warm for February, and people were eating ice creams on the beach.”
2adverbexceptionBy way of exception.
“Exceptionally, the library will stay open until midnight during exam week.”
Too few real examples of this word to estimate which sense is commonest.
exceptionally is a degree of unusualness.
Also accepted in games: exceedingly
From exceptional + -ly.
Etymology from Wiktionary, CC BY-SA