327,
I had the same situation with my ?01 Silverado. I did some researching on the WEB and found a recall site stating that Chevy, in an attempt to get better MPG, had set the shift point in the transmission really low in the RMP before going to second gear. Therefore if the driver were nursing the fuel feed they would not have enough momentum when going to second. (Sorry I tried to find that again, but no luck yet after a year.)
I did try driving with a little heaver foot on take off, and no it wasn?t hammer down

, the problem did not reappear.
The site also continued to state that Chevy was correcting the sifting problem as the vehicles come back in for maintenance. I do my own maintenance so I just called up my dealer a scheduled an appointment for him to do this modification for me. It took a whole 5-10 minutes.
FYI: I am having the same thing with my ?02, just not as hard. I plan to buy a Super Chip reprogrammer so I can adjust for the bigger tiers I am planning on buying and tune in any performance pieces I add. I will adjust my shift point myself at that time.
Hope this helps
Bow