You have set font-size for <p>, but you haven't used <p> tags. Try this:
Code:
<div id="shippingInfoMainContent" class="content">

<h2>Standard Ground (USA)</h2>
<p>Always Free Shipping<br>
Arrives in 2-7 business days</p>

<h2>2nd Day Express (USA)</h2>
<p> Starts at only $7.95<br><br>

Arrives in 2-3 <strong>business days</strong><br><br>

Not available for P.O. Boxes<br><br>

Shipping charges for 2nd Day Express will vary depending on the weight of items in your order. Shipping costs are shown and calculated before you checkout. Please proceed to checkout to see costs for your order. <br><br>

Shipping cost is non-refundable for undelivered, unclaimed, returned and refused packages, unless we made an error. </p>

<h2>International Customers</h2>
<p>We do NOT ship internationally at the present time.</p>

<h2>Refunds</h2>
<p>Unopened products in their original sealed packaging can be returned up to 30 days after the ship date for a full refund minus a shipping charge of $5.95 (per item - standard shipping, or $5.95 plus any additional shipping cost you incurred for using 2nd Day Express), which will be deducted from the credit we apply.<br><br> 

Any shipping cost you incur to return the product to us will not be refunded.<br><br> 

You can expect a refund within one billing cycle of our receiving your returned product.<br><br>

Opened packages cannot be returned. <br><br>

Please make your selections carefully as <strong>we do not offer exchanges.</strong></p>

<h2>Returns should be sent to:</h2>
<p>
Returns<br>
Order # (please enter your order number)<br>
5 Plant Ave<br>
Hauppauge, NY 11788</p>

<h2> *Please include your original packing slip.</h2>

</div>
(The gray text is the ZC-generated code that surrounds your custom text. You can use #shippingInfoMainContent as part of a selector if you need to make something unique for this page.)
Add to your stylesheet
#shippingInfoMainContent {margin-top: 2em;}
to space the h2 down from the main Shipping & Returns heading. Adjust the 2em to taste (1.6em, 2.3em...).

Sometimes using <br /> is necessary (like an address), and <br /><br /> can be much simpler than custom <p class="tightPara"> </p> tags which you then have to have a style rule for.