1) I post a receipt of the item, have a video drawing of the sweepstake, and post the tracking number of the package after it's sent out. Short of revealing the winners name, I don't know what other proof I can provide (although googling the user's usernames reveals quite a bit about them, I encourage them to change their usernames). I understand what you mean, on first glance I can see how people think the site is a scam.

2) I show how many people enter, so the odds are 1/(total number of entries). I was thinking of requiring a valid/unique phone number on registration and require the users to input the code I text them. Think of Craigslist / Chatroulette / etc.

I don't envision any people from Hacker News using the site on a daily basis. In fact, I posted it here as a "Show HN" and a whooping <10 people visited. There are people where an extra $25 means getting to take your daughter out to dinner when she announces she's engaged or an extra $100 means you get to pay your bills on time for the month (real winner stories so far). What really pushes me to work on the site every day is that even if the site fails to grow, at the end of the day, I've helped people without asking for anything in return.

I appreciate the comments.