In HTML, what is the opposite to <strong>?

To mark text as not emphasized or important, simply do not mark it up with the em or strong elements respectively.

Source: HTML 5: The small element

No, there's no opposite. Regular text would be the closest unless you create a custom css class like:

span.weak {
    font-weight: lighter;
}

Which would, of course, allow you to have markup that looks like:

This is some <span class="weak">very weak</span> text.

<strong> stands for “strong emphasis”.

There is also normal emphasis, i.e. <em> and of course no emphasis – normal text.

To deemphasise is not a common semantic need that has spawned an own, accepted typographic style so there is no special tag for it. You need to go the route via <span>s and CSS, e.g.:

This is is <strong>very important</strong>. You should remember it.
<span class="deemphasized">This, on the other hand, isn’t important
at all. Ignore it.</span>

Printed slightly smaller and with a lighter colour (assuming the normal colour is black, and the background is white):

.deemphasized { color: #444; font-size: 0.9em; }

No. The opposite of strong would be normal text.