Is it true that fat chickens lazy on laying eggs?

[SFBayArea]

My dad told me that in his childhood he heard that chicken cannot be fat or it will not be laying eggs. Is it true?
Is there a such thing as overfeeding chickens? They have food pellets available to them anytime and they roam in the back yard all day long and during the day I bring them vegetables and maybe some leftover from the kitchen. Am I overfeeding them?
My 9 chickens were laying 4-8 eggs per day, now it is 1-4...

 

[QueenMisha]

An obese hen will most likely continue to lay eggs, but her productivity will be reduced due to her unhealthy state, and her risk for many illnesses and diseases is significantly increased.

If you are only providing a good quality commercial layer pellet or crumble and scraps which make up no more than 15% of the diet, chances are your birds are completely healthy. The most fattening item I know of is scratch; any bird I've ever met who was fed a diet of more than 10% scratch has been, to some extent, obese. The same goes for hens frequently fed items which would be considered fattening for humans; French fries, bread or buns, chips, fast food scraps, etc.

What age are your hens? Any recent changes in your flock's environment? How's the weather there? Age, stress, and temperature can be some of the most influential factors in a hen's laying ability.

 

[SFBayArea]

They are 1.5 years. I got them (bought them with coupe) almost two weeks ago (will be two weeks this Sunday). So they moved from one more cooler location to my place which is probably 10-15 degrees hotter. However, they were laying very well all of the first week and started laying much less this week.
Do you think it is belated reaction to the move?

 

[QueenMisha]

They are 1.5 years. I got them  (bought them with coupe) almost two weeks ago (will be two weeks this Sunday). So they moved from one more cooler location to my place which is probably 10-15 degrees hotter.  However, they were laying very well all of the first week and started laying much less this week. 
Do you think it is belated reaction to the move?

Potentially - it could be related to either moving stress or the temperature change, and very possibly both. I've found it takes about a month after a significant change occurs for their cycles to settle down completely, and before then laying is usually hit and miss.

 

[SFBayArea]

Thank you