Hello,
To do that you'll have to edit the code of your emails via "Hikashop->System->Emails" and edit the code of the "HTML version" of your email to properly change the "cart" structure and display the total weight information, editing these lines will do the job :
<table class="w550" border="0" cellspacing="0" cellpadding="0" width="550" style="margin-top:10px;margin-bottom:10px;font-family: Arial, Helvetica, sans-serif;font-size:12px;line-height:18px;">
<tr>
<td style="border-bottom:1px solid #ddd;padding-bottom:3px;text-align:left;color:#1c8faf !important;font-size:12px;font-weight:bold;">{TXT:PRODUCT_NAME}</td>
{TXT:CUSTOMFIELD_NAME}
<td style="border-bottom:1px solid #ddd;padding-bottom:3px;text-align:right;color:#1c8faf !important;font-size:12px;font-weight:bold;">{TXT:PRODUCT_PRICE}</td>
<td style="border-bottom:1px solid #ddd;padding-bottom:3px;text-align:right;color:#1c8faf !important;font-size:12px;font-weight:bold;">{TXT:PRODUCT_QUANTITY}</td>
<td style="border-bottom:1px solid #ddd;padding-bottom:3px;text-align:right;color:#1c8faf !important;font-size:12px;font-weight:bold;">{TXT:PRODUCT_TOTAL}</td>
</tr>
<!--{START:PRODUCT_LINE}-->
<tr>
<td style="border-bottom:1px solid #ddd;padding-bottom:3px;">
{LINEVAR:PRODUCT_IMG}
{LINEVAR:PRODUCT_NAME}<!--{IF:ORDER_PRODUCT_CODE}--> {LINEVAR:PRODUCT_CODE}<!--{ENDIF:ORDER_PRODUCT_CODE}-->
{LINEVAR:PRODUCT_DOWNLOAD}
{LINEVAR:PRODUCT_DETAILS}
</td>
{LINEVAR:CUSTOMFIELD_VALUE}
<td style="border-bottom:1px solid #ddd;padding-bottom:3px;text-align:right">{LINEVAR:PRODUCT_PRICE}</td>
<td style="border-bottom:1px solid #ddd;padding-bottom:3px;text-align:right">{LINEVAR:PRODUCT_QUANTITY}</td>
<td style="border-bottom:1px solid #ddd;padding-bottom:3px;text-align:right">{LINEVAR:PRODUCT_TOTAL}</td>
</tr>
<!--{END:PRODUCT_LINE}-->
<!--{START:ORDER_FOOTER}-->
<tr>
<td colspan="{TXT:FOOTER_COLSPAN}" style="text-align:right;color:#1c8faf !important;font-size:12px;font-weight:bold;">{LINEVAR:NAME}</td>
<td style="text-align:right">{LINEVAR:VALUE}</td>
</tr>
<!--{END:ORDER_FOOTER}-->
</table>
<!--{END:VENDOR_LINE}-->
<!--{IF:PAYMENT}-->
<p>
<span style="color:#1c8faf !important;font-size:12px;font-weight:bold;">{TXT:PAYMENT_METHOD} :</span> {VAR:PAYMENT}
</p>
<!--{ENDIF:PAYMENT}-->
<!--{IF:SHIPPING}-->
<p>
<span style="color:#1c8faf !important;font-size:12px;font-weight:bold;">{TXT:HIKASHOP_SHIPPING_METHOD} :</span> {VAR:SHIPPING}
</p>
<!--{ENDIF:SHIPPING}-->
Note that you can also gather the weight of your products like that {LINEVAR:product.product_weight} but it won't be rounded and without the weight unit.
You'll also have to edit the "Preload version" of your email to properly calculate and load your customers order total weight.
Please let us know if you can accomplish this for us.
Sure we can do it as a custom work.