Why is honey more dense than water? I think it's because the molecules in honey are more tightly packed than in water. Would this be correct?
And the relationship between gravity and pressure in a fluid is that changing gravity then changes the forces a fluid's molecules exert to maintain static equilibrium since gravity affects its weight then the pressure in a fluid increases due to the forces going down and upward in the fluid. Is it fair to say that increasing gravity then also increases the density of a fluid which therefore increases the pressure in the fluid?
 A: Molecules in honey are not really more tightly packed than water molecules. In fact, it is pretty easy to estimate the molecular volume enjoyed by each of those two liquids without resorting to any fancy statistical mechanics or fluid simulation.
If you have the molar weight of a substance (how much do $N_A=6.02.10^{23}$ molecules weigh) and its density, you can calculate its molar volume, which easily gives you the average volume occupied by one molecule. In short:
$$V_{molecule}=\frac{M_{molar}}{\rho N_A}$$
Using $M_{H_2O}=18.02\text{ g/mol, } \rho_{H_2O}=1\text{ g/cm}^3, M_{honey}=180\text{ g/mol, } \rho_{honey}=1.415\text{ g/cm}^3$, I get:
$$\require{mediawiki-texvc}  V_{H_2O}=30\text{ Angstrom}^3$$
$$V_{honey}=211\text{ Angstrom}^3$$
So the honey molecules, although larger, can hardly be considered to be packed more closely together; they are contained in a much more spacious volume.
In fact the explanation for the density is almost more simple. Honey is essentially made of fructose and glucose. And a single of those molecules is WAY heavier than a molecule of water. So even if they are packed with a similar distance between them as in water, the result is still denser.
You can put it this way: the molecules are not packed more closely together but you can understand a larger molecules as a closer packing of atoms together. It is simply more efficient to get a lot of atoms together in a long string rather than in a lot of of little strings (or you would have to pack the little strings a lot closer to get the same final density)
In regard to your other question, increasing gravity does increase the pressure at the bottom of a layer of fluid. For most practical purposes tho, water is considered incompressible (which means its density does not increase with pressure. Or rather that you'd need crazy pressure levels to squeeze water)
A: The molecules in honey are long and complex sugar molecules. Even though the sugar molecules may not be packed close to one another, the number of atoms in each sugar molecule is significant, and if you look at the number of atoms per unit volume in honey (all the atoms in the long molecules), you'd find a lot more mass per unit of volume than the same for water. By definition, this means the density is greater for honey.
It is true that gravity will increase the density of a fluid at the region toward the bottom of the fluid, and this does indeed increase the pressure of the fluid in the same region.
In fact, the pressure at a depth $h$ in a fluid in a gravitational field is given by the Bernoulli equation, and for static fluids $$P(h)=P_0+\rho gh$$ where $g$ the strength of the gravitational field and $\rho$ is the density of the fluid. So gravity does indeed effect the density and pressure of fluids at certain depths.
