Thanks for figuring this out!
As written, it failed to multiply the weight when a customer purchased multiple of the same item, so I changed it slightly:
{% assign total_weight = 0.00 %}
{% assign temp_weight = 0.00 %}
{% for line_item in line_items %}
{% assign temp_weight = line_item.weight | times: line_item.quantity %}
{% assign total_weight = total_weight | plus: temp_weight %}
{% endfor %}
Also, Shopify appears to store the weight in grams (even though it is entered in lbs), so where I needed the weight (to the nearest pound) displayed I used this:
{{ total_weight | divided_by: 453.5924 | round }} lbs