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covalent character decreases as size of cation increases. i hope this hint is enough.
Whenever we deal with questions of character, it's useful to pull up an electronegativity Pauling chart (some period tables contain one). Luckily, Wikipedia has our back: http://en.wikipedia.org/wiki/Electronegativity#Electronegativities_of_the_elements
Anyways, covalent/ionic character is a bit tricky to figure out; we measure the difference in electronegativity of two elements bonding together and we use the following rule of thumb: if the charge is 0 (or a little more), the bond is non-polar covalent; if the charge is > 0 but < 2.0 (some references say 1.7), the bond is polar covalent; if the charge is > 2.0 then the bond is ionic. Covalent character refers to smaller electronegativity difference while ionic character refers to greater electronegativity difference.
Now, notice all of our bonds are with F, fluorine, which has the highest electronegativity of 3.98. This means that to determine character we need to consider the electronegativities of the other elements -- whichever has the greatest electronegativity has the least difference and most covalent character.
Na, sodium, has electronegativity of 0.93, so our difference is ~3 -- meaning our bond is ionic. Ca, calcium, has 1.00, leaving our difference to again be ~3 and therefore the bond is ionic. Be, beryllium, has 1.57 yielding a difference of ~2.5, meaning we're still dealing with ionic bond. Cs, cesium, has 0.79, meaning our difference is again ~3 and therefore again our compound is of ionic bond. Lastly, we have Sr, strontium, with an electronegativity of 0.95 and therefore again a difference of roughly 3 and an ionic bond.
Thus BeF2 is of most covalent character.