Different pumps "latch" onto the stem in different ways - are you sure you're securing it properly? Some have a lever, some a knob, some twist - make sure you're latching it on.
And, when you unscrew the valve, I hit the valve to release a bit of air - this seems to open up the valve to make that first pump easier.
And finally, some pumps are easier than others. I have to lean all my weight on mine too (and I'm not a very light person!) and I've borrowed pumps that take almost no effort at all.
Edit: Ooops, while I was typing my epic response, Cunninghamair said the same thing, but better!
Last edited by Pedal Wench; 07-07-2009 at 06:43 PM.
For 3 days, I get to part of a thousand other journeys.