Regarding weight: providing the boots give adequate support to the foot and ankle, and providing the sole of the foot is protected from impact strike with the ground, particularly stony surfaces, light weight is best. Every extra ounce of boot is extra weight to be lifted by the leg at every step, which increases tiredness.
Regarding waterproof lightweights: I bought a pair of waterproof suede-and-nylon boots for general summer walking. I didn't specifically want waterproof ones, but these were available and the price was right. I had previously read in walking magazines that waterproof boots are hotter to wear, and with these boots I can confirm this is true. If I wear them in summer with ordinary sports socks on my feet, when I take the boots off, you can almost wring the socks out. It was never that bad with their predecessors (or the ones before that, or the ones before that).
The real joke is, they are NOT waterproof, not by any stretch of the imagination, they let almost as much water in as a pair of sandals haha.
So, for serious walking, in either wet weather or in rough wet terrain, I prefer to use Seal Skinz waterproof socks, but they are a bit pricey at around £22 and in your case not worth the extra cost if they're not going to be used much in the future (I presume you're having to pay for all your daughter's gear, like any dad!)