EDIT: As @coldvod mentioned, I'm also confused as to what you meant about the pull start feeling weak.
When the engine was running, did it just die or did you kill it with the kill switch?
A 2 cycle engine can vibrate pretty aggressively so make sure the spark plug is tight and you aren't losing...
If you have been tuning it with the needles on the carb than the very first thing I would do is replace the plug.
Tuning by adjusting carb needles can foul the plug.
Is the engine turning over when you pull on the rope? If it does then you should get spark.
I would also make sure the kill switch...