Is “influence on” or “influence over” correct in this sentence

“That is typical of you” is exactly what “You would!” means in this context. It is listed in some dictionaries, though it can be a little hard to find among the many other meanings of would; for example Cambridge lists it as

would modal verb (FREQUENCY) (…) disapproving used to ​suggest that what ​happens is ​expected because it is ​typical, ​especially of a person's ​behaviour:

"Madeleine called to say she's too ​busy to come." "She would - she always has an ​excuse."

This is closely related to the meaning explained just above: would can express something habitual. For example

He would always ​turn and ​wave at the end of the ​street.

means the same thing as “He always turned and waved …” but the use of would stresses the fact that it's a habit.

As for what you read in Urban Dictionary — don't mistake UD for a useful reference. A lot of what it contains is just what one person decided to add and doesn't mean that anybody else would understand. I, for one (admittedly not a native English speaker), have no idea what why “you would” is supposed to be annoying or this “I did forget”/“but really” business is supposed to mean (maybe it implies that “you would” was used sarcastically?).

While "although" and "despite" have similar meanings, there is a difference in how we use them.

Although is a subordinating conjunction and it is followed by a clause (subject-verb structure).

Although he worked very hard, he didn’t manage to pass the exam.

Despite is a preposition and it is followed by a noun or a pronoun.

Despite the pain in his leg he completed the marathon.

In your sentence, "being" is a gerund which is the noun form of the verb "to be", So you should use despite.

Despite being an unknown underdog, he won the championship.

The answer would be "although" if your sentence were like this:

Although he was an unknown underdog, he won the championship.

If you remember the meaning of "although" as "despite the fact that", it will be easier for you to choose the correct answer.