Maybe you can fix it
If you can, cover. Yeah, it's dishonest but not necessarily a bad thing. You said you love horseracing/baseball/salsa dancing/taxidermy/needlepoint/speed metal and don't know the first thing about it? Get online and learn everything you possibly can about horseracing/baseball/salsa dancing/taxidermy/needlepoint/speed metal. You might actually discover a new interest. If not, you might have to fess up or you'll find yourself feigning enthusiasm through endless hours of dance classes or, worse, Slayer.
Similarly, you might not be able to turn the clock back 10 years, climb a mountain or get a speedy doctorate (though you could try saying you called Steve and he was just too busy, then later claiming you just "drifted apart"). In that case, try confessing. After sex is usually best. Simply say "I'm actually a clerk/accountant/fry cook. I just wanted to impress you and I got carried away. I'm sorry," and hopefully they'll be flattered.
You snooped and found something you didn't like
We all look for clues to what a new person is about. They step out to get some food and we go through their medicine cabinet, fridge, bookshelf…email? Encrypted computer files? Whoa. You should have known when to stop and now you've found something you're not happy about. Serves you right.
Maybe you can fix it
Unless it's something you need to call the cops about, shut your mouth. Take it from someone who's been there. Until you're married or common-law (and even then it's rare), the snooper is NEVER in the right. Never say anything about it and hope you can live with it. If you can't, maybe you need to take a hike. At least now you know and aren't running about blissfully unaware. If you can't control yourself and absolutely must confront the person, be prepared to feel like a total tool when they point out that you had no right to be snooping. This is during the beginning of a relationship. As things progress you should get more and more access to their lives and stuff, within reason.
You cried after sex
This apparently happens to a lot of people and, if you're not depressed or otherwise unstable, it's probably due to a fluctuation of hormones and release of tension. Sex can also have the other effect. I dated a guy who broke into maniacal laughter every time he came. EVERY TIME. I loved it. But it can make things a little awkward if someone you barely know is lying next to you wondering what all the blubbering is about.
Maybe you can fix it
Explain exactly what I just told you. Who's gonna argue with science? Then, it might be amusing to make yourself laugh. As Madan Kataria a.k.a. "The Guru of Giggling" and founder of Laughter Yoga would tell you (and has told me in the past), if you force laughter, you'll often find yourself actually laughing. And the great thing about laughing is it's contagious. So, maybe your bed buddy will wind up guffawing with you and everything will be awesome. Alternately, they'll think you're a freakin' psycho. But then, you know you're not, so who needs them?
And that's what it comes down to. Relax. To err is human and true love will overcome. Remember that when you're standing outside their house in your slippers, going through the garbage. Or staring at your phone with a wicked hangover wondering who you called last night.
As Slotnick says "One mistake can't blow something that's really meant to be."