I use PowerTip big-time... consuming thousands of pieces a month. Never any problems interfacing to PICs or using with PBP. PC1602F (which is actually a 16 x 2) is very price competitive and perhaps the one to consider.

When I was in China a few weeks ago, I visited Tri-T, who claim to offer a direct compatible unit to PowerTip (TMBC16265SP) but with Backlight at the same price as PowerTips standard reflective unit. The sample I walked away with was excellent. The first batch of 200 is clearing customs at the moment and I'll let you know if they're all as good as that original sample by the end of the week.

Moving back to the weights...

I see no problem detecting the weights being lifted, as you can have a photosensor on the floor with the weights covering it. At the lift end, I'd use a IR emitter/detector (of the sort found in TV remotes). Modulate it at it's working frequency (usually around 38kHz) and detect that. It should make it pretty much immune to extraneous light, flash-photography etc.

You may want to change the Olympic Timer software so that you can only START the clock ONCE following a RESET. As it stands, once it's stopped, you can start again and continue timing from where you left-off.