Good rule of thumb I use all the time for back of the envelope calculations:
First of all, I'm going to reference specific gravity because it's unitless. Density can be measured by any combination of units of mass and volume, but you must specify units. Kilograms per cubic meter are the SI unit, we often use grams/milliter in Chemistry for convenience, but there's no reason why you can't use stones per bushel or any other crazy combination of units. To find specific gravity, you take the density of whatever substance you're measuring and divide it by the density of water. That makes the specific gravity of water 1.00 by definition. BTW, water is close enough to 1.00g/mL for many purposes.
In any case, as said by definition the specific gravity of water is 1.00.
Most non-halogenated organic solvents fall somewhere in the .75-.85 range.
Most halogenated organic solvents are around 1.2-1.5.
Back when I was a Chemistry stockroom manager, among other hats, I'd often help unload the UPS truck. We'd often get solvents in 20L metal cans, which is a bit over 5 gallons. We would order them for the stockroom(especially acetone) and research groups would often do bulk orders a few times a year. There could be times where there would be 10-20 cans of solvent in a shipment. BTW, shrinkflation and all that, a few years back a lot of companies downsized to 18L to hold prices. 18L is almost exactly 5 gallons.
For a lot of the common lab solvents that would get ordered this way-acetone, methanol, hexane, ethyl acetate, toluene, etc a 20L drum would weigh about 35lbs. Dichloromethane and Chloroform would be more like 50-60lbs. Suffice to say if you weren't looking at the labels, you'd KNOW when you picked up a drum of halogentated solvents(and considering that most just had a simple wire bail handle, they weren't the most comfortable thing to carry). We'd also get 200 proof undenatured ethanol in 5 gallon plastic bottles, but that came through a different source(to be able to get it tax free).
As said too, density has nothing to do with whether or not something will mix with water. I'm aware of 7 common organic lab solvents that are miscible(will mix in any proportion) with water. Those 7 are methanol, ethanol, isopropyl alcohol, acetone, dimethylsulfoxide(DMSO), acetonitrile, and tetrahydrofuran(THF). They're not usually cited in "misbilitily" lists, but I'm pretty sure the small poly-ols like ethylene glycol, propylene glycol, and glycerin are also. The key with all of these actually is that they are able to hydrogen bond readily with water, and their non-polar portions aren't so large as to prevent this.
Most other common solvents-especially hydrocarbons-are too non-polar. With that said, there's often SOME degree of water solubility especially with things with some ability to hydrogen bond like diethyl ether. Density does determine which layer is on top when two things form a biphasic mixture-non-halogenated solvents generally are on top of water, and halogenated are on the bottom.