Lights dim when accelerating?? 2002 LT

Anybody have a clue what might make my lights dim and security light come on in my 2002 1500LT when I give it any gas?? My voltage meter doesn't move and all the wires to the battery and alt. seem fine. Any clues would be great. Thanks

Usually that's a sign of a weak battery. Go to the dealer and have them do a load test on the battery, or you can go to a place like Auto Zone, they will check it for free.
A friend at work had to replace the battery in his 2500HD after only 13,000 miles!!! Same simtoms as yours.