Wookies live upwards of 400 years, Chewie is 205 during the OT, so about 235 during Force Awakens. Yoda was 900 years old when he died.
What I take away from this is that races with longer lives tend to live their lives differently than humans and other short lifespan races. Wookies still live in forest tree houses. Whether on purpose or because of subconscious authorial assumptions, longer lifespan races tend to live life more slowly and 'in tune' with nature. Additionally, on Earth, animals with longer lifespans tend to breed and multiply more slowly. This would naturally slow down any expansionist behavior these longer lived races would exhibit.
>In summary, we are the rabbits in the eyes of the Yodas/Wookies/other long-lived races.
Also, The Old Republic was dominated by human races and it appears that their planets comprise the majority of the "core worlds". This would have also been further exacerbated by the Empire's xenophobic policies, leading to a place like Mos Eisley in the Outer Rim to have a more racially diverse makeup than a core world. The Empire's 'influence' would not easily be absolved in a 30 year period, leading to humans still being the dominant force in the galaxy.
Lastly, from a practical standpoint, it is easier and cheaper for a production company if the majority of the primary cast is human/humanoid. Us human consumers find human characters more relate-able, thus causing the stories that are written to focus more on human leads.