The pilot of a LSA ran off the end of the runway when he fast on long on a downhill slope with a tailwind.

Narrative

Ten miles from my non-towered destination I called CTAF to announce my arrival and intentions to over fly the field at 1500 AGL; which I did. The windsock was alongside the runway and was difficult to see. Its shadow; however; seemed to indicate a cross wind; so I continued upwind; downwind; base and final for RWY XX; a 3300 foot runway. The airspace was completely deserted; so no active runway was evident.The approach was a little high; so landing started out long. This aircraft tends to float; which it did; but with 3300 feet I was not too concerned. It took a long time to touch down and I seemed to be going very fast. The LSA has a single hand brake for both wheels which I started to use aggressively. It veered to the left; I recovered; and continued to brake skidding the tires several times. The runway went downhill at that point; further aggravating the situation.Soon I was running out of runway and still going quickly. I couldn't stop in time and exited the runway into the large gravel and weeds at the end of the runway traveling an estimated 10 knots. I turned the aircraft in a 180 without stopping; applying power gingerly because of the gravel and got back on the runway.I stopped in transient parking; and inspected the aircraft with no noticeable effects other than grass in the brake shoes. Then I noticed the wind sock; and it was indicating about 10 knot tailwind for [the runway I landed on]! I assume the wind changed during the time I made the approach; but I'm not sure because the windsock was hard to see at 1500 AGL.Human factors issues: Not sure of the windsock indication; and not following up on that. Not having a physical landmark at which to go around. Not looking for the windsock on final? Too focused on getting energy under control. Not noticing A/FD indicated a 0.9% slope (down for [the runway I landed on]. No training in going around at just before touchdown; or when past some landmark. With no traffic in the area; why not make a low pass? That never occurred to me. I am in need; and will accomplish; practice in all of the above areas.