It would appear that you're looking to cycle through the contents of the smaller file

With `awk`

 awk 'NR == FNR{a[++i]=$0; next}; 
 {print $0, a[FNR % i? FNR % i: i]}' smaller_file larger_file

And `python`

 from itertools import cycle, izip
 with open('larger_file') as f1, open('smaller_file') as f2:
 z = izip(f1, cycle(f2))
 for l, m in z:
 print l.rstrip('\n'), m.rstrip('\n')