Honestly, this really downplays Tawny. I have a half-decent bottle of a 2011 LBV Tawny Port, which is about as low quality as I will drink. I opened it probably six to nine months ago, and it's still pretty good, though obviously not at its prime.

Traveling around Spain and Portugal you can find Vintage Ports that cost about $25 and will taste absolutely amazing (though I try to stick to above 20-year oaked tawny blends). Quite a few are not very sweet, and not very heavy. Also, Vintage Port has a considerable shelf life. The oldest currently available vintage is 1815.