You don't have to speculate.

All time:

https://blockchain.info/charts/blocks-size?timespan=all&showDataPoints=false&daysAverageString=1&show_header=true&scale=0&address=

one year:

https://blockchain.info/charts/blocks-size?timespan=1year&showDataPoints=false&daysAverageString=1&show_header=true&scale=0&address=

On a one year basis looks fairly linear.
On an all time basis you can see some exponential growth.

It is almost entirely driven by this graph:

https://blockchain.info/charts/avg-block-size?timespan=all&showDataPoints=false&daysAverageString=1&show_header=true&scale=0&address=

which is the average block size. More transactions per minute, larger average block size.