First, one must understand what tone is. According to Brooklyn Academics' Literary Term page, tone is defined by the following:
By looking at the two stanzas of "Design" one can immediately see distinct differences.
The first stanza holds descriptions of the spider that Frost has come upon.
I found a dimpled spider, fat and white,
On a white heal-all, holding up a moth
Like a white piece of rigid satin cloth--
The second stanza is very different. Frost is offering questions on the existence of the spider, its size, and its movements.
Therefore, the first stanza offers a tone which proves to be sure. Frost knows exactly what he is looking at; he is able to describe the scene in detail.
The second stanza is where Frost begins to contemplate the spider's existence. Here, the tone becomes questioning and one of wonder. Frost can no longer explain, the the same immaculate detail, the spider.