if play is side to side then the bearings are likely to have developed a bit of slop. This is easy to fix but requires some quite thin spanners for the job and some fairly careful jiggling about. LBS if you're not sure. Doing the bolts up extra tight won't make any difference to this. But if you don't have one already, a decent ring spanner will help as it won't slip so easily if you do put your foot on it.
if play is side to side then the bearings are likely to have developed a bit of slop. This is easy to fix but requires some quite thin spanners for the job and some fairly careful jiggling about. LBS if you're not sure. Doing the bolts up extra tight won't make any difference to this. But if you don't have one already, a decent ring spanner will help as it won't slip so easily if you do put your foot on it.