Losing 10 lbs will take a LOT more than a simple frame swap. To even hit 25 lbs will require some studied and educated care in selecting such things as cranksets and wheels.
But before you even go there and start spending gobs of money lets stop and consider a couple of things. You're talking about trying to shave off about 1/3 the weight of the bike. But the bike doesn't ride itself. You're typically along for the ride

So what do you and the bike total out to for weight? Let's say you're 180 in your socks for the sake of argument. Add on another 5 to 7 lbs for clothes and shoes. Now add the 33 lbs of bike. That's 218 to 220 lbs total. You're going to shave off a measely 10 lbs at the cost of around $500, give or take, for a lowly 10/220= 4.5% difference. Doesn't seem like so much now does it......
So let's look at what will REALLY make a difference. First off for street riding the tires have a ton of effect. If you're plodding along with knobbies then switching to some 1.25 to 1.5 inch smooth slick road tires that run with high pressure will make it seem like Lance Armstrong just gave you a blood transfer. The smooth low drag high pressure shape combined with the drop in rotating weight will make the bike seem like it lost more than your 10 lb target. And realistically this is the only mod you really need to make.
Next, the picture makes it look like it's a very sit upright style of bike. And that suspension seatpost has to go. That'll shave a lb off but more importantly it'll sit you on the bike more solidly so you can put the power to the pedals more effectively. Next is to angle the bars somewhat down and forward so you've got a slight cant into the oncoming wind. That'll again put your center of gravity more over the cranks so you're able to put the power into them without your balance pushing you back onto the saddle instead of down onto the pedals. And the other thing is to fit the saddle height so that your legs are just shy of your knee going over center and locking. You want your knee joint to almost but not quite be fully extended as your foot passes the bottom of the pedal stroke. If you're like a lot of casual riders you may have your saddle set so that you can touch the ground while still seated. This is by far the worst thing you can do for efficiency. Setting the saddle to the correct height is a huge first step. Along with that you are likely going to find that the soft cushy saddle is now too wide and the rear of your thighs is hitting the flare at full extension and levering you forward onto the horn of the saddle. If/when you notice this it's time to shop for a more narrow saddle. Yes it'll hurt if you sit on it for long. But when riding for performance such as you're looking for you are not supposed to be using the saddle so much to sit on as to just locate your backside on the bike. Your legs should be supporting much of your weight either while pedaling or coasting.
Any of this helping? What you really need is for someone locally with knowledge of fitting mountain bikes to riders for performance riding to work with you. The new tires and correct setup are the only upgrades you need to make your San Anselmo into a rocket... well those and some exercise....

On the other hand if you were to splurge on a lighter frame, lighter wheelset, lighter crankset, lighter seat post and lighter bars to shave off 8 or 9 lbs and still try to ride with the knobbies or poor setup and body positioning then you won't feel a dime's worth of improvement.