Why does my rear cassette feel like it's jumping when I put pressure on small cog? I just gave my bike a going over with new bearing cages in the BB and a new chain. After putting everything back on I indexed the gears - finally getting the hang of the front but first time indexing the rear derailleur. It all felt fine on the stand, but when I go uphill with the rear gears on the lowest cog (6), when the pressure is on the pedals I get a weird jumping, clunking thing keep happening.

Now I was told this could be because my rear cassette is worn, but I've had a close look and done the brake-on-pedals-pushed test, no play on the chain on any cog, looks fine to me, how does this look to you : The mech doesn't look bent, either. Is it just that I need to get my indexing in better form, and need to perfect the cable tension, or are there other causes for this (like maybe wear on the drive cogs - do they look like they need replacing below?)?
Those teeth are severely worn, just by visual inspection. Try a new cassette, chain rings, and chain. (Don't try changing just one.)

It could have been the grime that was holding the worn system together, and when you cleaned it all the play now shows up. In the future, if you replace your chain more often you can make the chain rings last longer.