At first ensure that the competent cells you used for cloning has high competency at least 10^8, the other thing u can try is giving polynucleotide kinase treatment to your inset and setting up ligation reaction simultaneously in 1:3 , 1:5 ratios it may help.u can also try using quick ligase as an alternative.

I would suggest using electroporation instead of chemically competent cells. Plasmid size has a pretty strong negative effect on efficiency of transformation, but much less so with electroporation. 

6.5 KB plasmid is not preety big for a plasmid , i have been sucessfull with plasmids as large as 8 kb.Also electroporation is a subject to availablity of the instrument your institute.One important point i want to highlite is -1) do u use positive control i.e native ,undigested vector as transformation ctrl. (2) do u use negatice ctrl, double digested vector ....if u find colonies on your positive ctrl the problem may be with your ligation.

all d best .

Heat inactivate the ligation mixture before transformation, this should improve the transformation efficiency many folds. Also, try using ultra competent cells for maintaining big plasmids, like XL-10 gold or XL-1 blue, both from Stratagene.

You can also de-salt the ligation mixture using Microcon's DNA FastFlow spin columns, then transform.

Also, after transformation, and 1h incubation @37C, mildly centrifuge the culture, discard supernatant carefully, and then resuspend the pellet in 100microlitres of fresh medium and plate it on the agar plate containing the half of the recommended concentration of antibiotic (Eg. if recommendd concentration is 100ug/ml then use 50ug/ml in the nutrient agar). Let us know/update if it helps.

Goodluck...