You need to remember that the coefficients are dependent on the scale of the variable. Consider a logistic regression where x1 is height (of a person) in inches, what happens if you change this to height in meters or height in milimeters? The coefficient changes (and what a 1 unit increase means changes), but the overall effect of the variable will not change (unless there is major changes due to rounding).
I have had regressions where the coefficient for the most important variable was close to 0 (once it even printed out as 0.000 due to rounding), this is because the variable is something like the dose of a drug in milligrams and differences are in 100s or 1,000s of milligrams, so a one milligram increase is not very meaningful (for those I often recode the variable so that a 1 unit increase is more meaningful).
Sometimes people will standardize all the predictor variables so that a 1 unit increase is a 1 sd increase. This can make the coefficients more comparable, but sometimes the standardized variable becomes less meaningful.
You also need to consider relationship between the potential predictor variables.