loop through an entry's "related entries", grouped by category
Try this:

{% for category in categories %}
    &lt;h2&gt;{{ category.title }}&lt;/h2&gt;{# spit out the Category #}

    {% set entries = craft.entries.section('news').relatedTo(category) %}
    {% for relatedEntry in entries %}
        {{ relatedEntry.title }}
    {% endfor %}
{% endfor %}


See the set entries = ... line.

I am retrieving the entries that are related to each category as it loops thru each category.