It is similar to the concept of "the more, the better" in English.
The more celebrity the person is, the bigger (or the more) the stress he or she may have.
or
The more famous the person is, the bigger (or the more) the stress he or she may have.
If the sentence is just
有名人であればストレスも大きいのではないだろうか。
is simply: if the person is a celebrity, the stress he or she has may be big. By adding "あるほど”、the meaning changes to the first sentence above.
I hope this helps.