So it's a 10-team league, right?
Looks like your league re-sets waivers each and every week based on first-to-worst order of the standings. I'm not sure if it's reset based on your weekly performance or your overall record, so you might want to check on that.
Either way, it basically means you lost the #1 priority when you didn't put in a claim before the first week (after your draft, players were probably locked for a certain period of time and then went through waivers before becoming free agents for first-come, first-served (FCFS) pickups. After you didn't use the No. 1 spot there, you ostensibly "lost" it unless you finished last after the first week. Since you finished 9th, you get the second waiver spot (again, check to see if the waivers reset each week based on weekly record/points scored, or for the combined record/points for the whole season, as that will have an effect on how things play out after this week).
I'm a bit confused about the status of Henderson - is he on your roster, or was he locked until this Wednesday because his game had started (more likely, but I wanted to be sure)? Either way, you should/would be able to cancel your claim for him before the date with no penalty or threat of losing the spot as far as I know. Since you have the No. 2 spot and want Newton, you should be able to set up some sort of prioritized list (I'm not familiar with NFL.com's specific game, but this is pretty standard) where you can make Newton your first priority pickup and then Henderson or whoever else your second. That way if the guy with the No. 1 ww claim picks Newton you still get your second choice.
As long as they reset every week, regardless of the reason, I'd recommend using your high claim on either Newton or someone like Tate, Cadillac Williams and then go from there. Since you'll roll to the bottom of the list after that, you can certainly make more claims, but you'll probably only get one premium guy, so make sure to set your order accordingly and get once big fish before scraping the bottom of the barrel time starts ...
Hope this wall of text helps