Purely ionic bonds are hard to find. Almost all bonds have some covalent character. The amount of covalent character can be estimated by comparing the Pauling electronegativities of the bonded atoms, as explained by Mike H already. The more similar the electronegativities, the more covalent character the bond will have. The simple rules you learned about electron "transfer" or "sharing" are simply guidelines that help you understand the limiting cases. For many molecules, the actual bonding situation is quite close to a given pure electrostatic or pure covalent cases, but sometime it is not. The classic example is hydrogen fluoride (HF) ... would you say that is covalent or electrostatically bonded?
Your ideas about silver being "heavy" are not proceeding along the right track. For example, gold chloride is soluble, and gold is in the same group but is much heavier than silver.
Solubility equilibria exist for all salts, whether or not we describe them as "soluble". In real terms, what determines whether or not a salt is soluble is whether or not the Gibbs free energy of the system (solute and solvent) is lowered by having the solid salt dissociate into the solvent. Remember, for a process to be spontaneous at a given temperature, the Gibbs free energy change: \Delta G=\Delta H - T\Delta S must be less than zero. In all cases, the entropy of the system is raised (\Delta S > 0) when the salt dissolves, but sometimes this is counterbalanced by a large enthalpy penalty (\Delta H > 0). Basically, the salt crystal has a large lattice stabilization associated with the organization of so many charged particles into a very favorable structure, so sometimes (particularly when you have multiply-charged ions) it takes more free energy to break the lattice apart than is regained from the positive entropy change associated with the dissociated state at the appropriate temperature, and so the dissolution process is not spontaneous.