Your loop should point to the tags property of your blog, not the blog entity itself.
{% for tag in blog.tags %}
or
{% for tag in blog.getTags() %}
Furthermore you mustn't join category and tags because you get the related relationship entities via the corresponding properties of your blog entity. they will be proxy-loaded when you access them in your twig template.
I think it should be enough to pass only a BlogCollection to the view and then do
{% for blog in blogs %}
{% for tag in blog.tags %}
...
{% endfor %}
{% endfor %}