Do they? I'll have to take your word for it! Assuming this is true, there are potentially many ways in which weather could affect the outcome of a cricket match. These include: the state of the wicket, the run of the ball over the outfield, and the light and the ability of the batsman to see the ball.

In "An experimental study of cricket ball swing" Bentley et al show that weather has very little effect on ball swing or reverse swing - less than 2%. So this looks like it can be ruled out as a reason.

The simplest reason might be that the game needs lack of rain and good light to be played...and that disruptions in play are not condusive to winning. In their paper "Effect of Toss and weather on county cricket championship outcomes", Forest and Dorsey found that "the probability of either side winning declines rapidly as the duration of weather interuptions increases." They reached this conclusion through regression analysis, and I get the feeling that a cricketer is unlikely to take such a scientific view of things. Given the amount of superstition in sport it might be best to ask this question of a sportsman rahter than a scientist. Confidence plays a big part in performance. If a bowler feels that the ball flies better in good weather this could perhaps affect their performance. Or perhaps they have an inherent fell for what the regression analysis found and just know that if they want to win, it's best to play in good weather?

I agree with the previous answer for the most part.  But it is largely a function of the climate.  In Blighty it is not a lot of fun playing in a Scotch mist. In the Karoo or a Town Like Alice it is not much fun playing on a 45C summer day on a dust pitch and dodging the occasional oven-blast dust devil. The bar would be congenially warm in the one case, and congenially cool in the other (though dusty!).

The wetness of the outfield pitch can make it considerably harder to score runs. The ball doesn't bounce as far through wetter grass. Actual rain makes it harder to watch the ball as it is bowled towards you at 70+mph. A softer wicket can also make the bounce of the ball deceiving - you might expect the bowler to bounce the ball considerably higher but because of the softness of the ground it is a very low bounce, catching the unsuspecting batsman who has his bat in the air offguard. Running between the wickets to score runs becomes more difficult and the batsmen are more prone to slipping (and thus missing the ball or being run out).

Or possibly most cricketers are fair-weather sportsman and don't like suffering the elements - especially for 7 hours.

As a lifelong player, and scorer of many ducks, I can offer a more definitive, if somewhat anecdotal reasoning. In order of priority.

 1. To hit the ball the batsman must see it well, and quickly.  This requires contrast of the ball against the background, hence sightscreens and presumably better light provides better contrast and thus a quicker pick up of the flight, length and line (the MCC for example are now experimenting with pink balls in the one day game as the white ball very quickly becomes dull). 

2. Overcast conditions help the ball swing.  Most club level bowlers can’t really swing it, but if they can, the effect can be devastating (the science of swing is very complex and not fully explained) .  Just take a look at Jimmy Anderson on the Second day of the Edgbaston test 2009 for a master class .

3 As already mentioned a slow outfield means less runs.

The correspondent SciFI mentions some other minor reasons too, although the state of the wicket is more a feature of preparation (or lack of it) and weather in the previous days rather than at the time (unless it’s raining and it’s an uncovered wicket).

For the bowler, its more complex (as I mentioned most club players don’t swing the ball) so for them its more about the state of the wicket than overhead conditions as club pitches can vary from a featherbed, a bunsen to a minefield (see http://static.cricinfo.com/db/ABOUT_CRICKET/EXPLANATION/CRICKET_TERMS.html. 

To add a number or two, par scores in a 40 over game on our home pitch can vary from around 140 (soggy, overcast, wet week before) to nearly 200 (hot dry spell) depending on all these factors.  Hope this helps