Question
QUESTION: This is the first year I tried growing burpless cucumbers  They are growing fat
and round like a melon   what's going on?

ANSWER: Dear Debbie,
Burpless cucumbers are hybrids.  This is one of the "side-effects" or negative results of hybridization.  When various specimens are crossed to avoid one problem it can potentially make new ones.  I avoid hybrids if at all possible.  
Kind Regards,
Kindred
www.eingedi.us

---------- FOLLOW-UP ----------

QUESTION: Are they edible?

Answer
Debbie,
I think they are, they sound like the hybrid mix may be some sort of melon or something.  I don't think they'll hurt you, they just aren't quite the regular cuke.  They won't make pickles, but they should be fine in salads or just sliced.
Kindred