Stabilize, steady, poise, balance, ballast, trim are comparable when they mean to maintain or cause to maintain position or equilibrium.
Despite their agreement in basic meaning they vary widely in their implications and in their range of application and are seldom interchangeable.
Stabilize is used chiefly in reference to something which is fluctuating or is subject to fluctuation and which requires either external aids or regulation.
Steady is used chiefly in reference to something which is losing its customary or necessary stability or equilibrium and is demonstrating instability (as by rocking, shaking, fluttering, or tipping).
Poise is used chiefly in reference to something that maintains its equilibrium perfectly under adverse conditions or in opposition to external forces (as gravity); it implies a proper distribution of weight with reference to the supporting medium (as air or water) or to the part (as a base, a foot, the hand, or a column) that bears the weight.
In extended use, when employed in reference to the mind or spirit, poise implies either acquired control over the faculties or an inner serenity that enables one to remain steady or impervious to disquieting or disturbing influences.
Balance also implies an equilibrium that is the result of the proper distribution of weight, but it carries none of the suggestions of sustained position or equilibrium so strong in poise; thus, one balances a boat by adjusting its cargo so that there is no excess weight at any one point, and one balances a flywheel by removing portions where the weight is excessive or by adding weight in its lighter sections, but in either case the equilibrium may be lost if the cargo shifts or a section of the flywheel alters in weight.
Though both balance and poise imply that the thing affected is steadied, balance often carries so strong an implication of uncertain equilibrium that it suggests wavering or rocking.
Ballast is used in reference to what needs to be held down because too light or too buoyant; it implies the addition of something heavy or solid enough to ensure stability.
Ballast is occasionally found in extended use with reference especially to the mind and the moral character that might otherwise suffer from volatility, frivolousness, or unwieldiness.
Trim is chiefly nautical; it implies proper balancing of a boat or ship so that it sits well on the water or fulfills any of the conditions that make for steadiness in sailing.