In The Scarlet Letter, what effect does Reverend Dimmesdale’s guilt have upon his popularity in the colony?

The part of the novel you need to re-visit to answer this
question in Chapter 11, entitled "The Interior of a Heart." This is rather a sinister
chapter as it talks about the way that Chillingworth plans to psychologically encroach
on Arthur Dimmesdale's privacy and space, probing into the very centre of his soul to
discover what deep and dark secret oppresses him so
badly.

However, as you indicate, the severe impact of
Dimmesdale's guilt does have an impact on his work as a minister. Consider what the text
tells us:

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While thus suffering under bodily disease, and
gnawed and tortured by some black trouble of the soul, and given over to the
machinations of his deadliest enemy, the Reverend Mr. Dimmesdale had achieved a
brilliant popularity in his sacred office. He won it, indeed, in great part, by his
sorrows. His intellectual gifts, his moral perceptions, his power of experiencing and
communicating emotion, were kept in a state of preternatural activity by the prick and
anguish of his daily life.

It
is his guilt that allows Dimmesdale to have "sympathies so intimate with the sinful
brotherhood of mankind." "His heart vibrated in unison with theirs," we are told, making
him accessible. Part of his success, then, lies in the fact that he himself identifies
himself as a sinner and recognises the truth of that fact in his own life. This gives
him no arrogance or pride when he ministers to those who are like him. Such a manner and
approach to people in spiritual need endears him to them, making him immensely
popular.