Dont forget to backup first, incase something nasty happen.
Here is a tweak how to show product weight on prestashop 1.5.3.1 product page :
1. Go to your prestashop themes folder, like themes/(your names)
2. Search and open product.tpl file with your favorite text editor (like notepad, notepad++, or sublimetext2)
3. Search for following code :
<!-- left infos-->
<div id="pb-left-column">
<h1>{$product->name|escape:'htmlall':'UTF-8'}</h1>
{if $product->description_short OR $packItems|@count > 0}
<div id="short_description_block">
{if $product->description_short}
<div id="short_description_content" class="rte align_justify">{$product->description_short}</div>
{/if}
{if $product->description}
<p class="buttons_bottom_block"><a href="javascript:{ldelim}{rdelim}" class="button">{l s='More details'}</a></p>
{/if}
{if $packItems|@count > 0}
<div class="short_description_pack">
<h3>{l s='Pack content'}</h3>
{foreach from=$packItems item=packItem}
<div class="pack_content">
{$packItem.pack_quantity} x <a href="{$link->getProductLink($packItem.id_product, $packItem.link_rewrite, $packItem.category)}">{$packItem.name|escape:'htmlall':'UTF-8'}</a>
<p>{$packItem.description_short}</p>
</div>
{/foreach}
</div>
{/if}
</div>
{/if}
4. Below last {/if} code, add these 4 lines of code.
<div class="product_weight">
{l s='Product weight: ' js=1}{printf("%.3f",$product->weight)}
 {Configuration::get('PS_WEIGHT_UNIT')}
</div>
5. Dont forget to save and remove your cache. After that refresh the browser.
PS: if you dont want to display decimal on the product weight, you could edit the "%.3f", so it will be like "%.0f"