It's perfectly normal for early tests to show very faint, as the hormone level is low to begin with. Any line, however faint, is a positive reading and means you're about 99% likely to be pregnant. If your second test looked weaker than the first, it might be because you tested at a different time of the day (urine is stronger earlier in the morning). I wouls think it's extremely unlikely that you lost the pregnancy if you haven't had any bleeding or other symptoms. It's likely that if you re-test a couple of weeks later, the line would be darker.

I know with my daughter, I got a positive result at just 3.5 weeks, or 1.5 weeks after conception. That was a very faint line, but 9 months later it was an 8lb13oz baby!

Anyway, try not to stress too much and I hope you get good news at your appointment.