A barrow wheel that wobbles is usually the nut
I was moving a load of gravel in October and the wheel started to weave. The pan leaned. I thought the tyre was soft. I tipped the load, squeezed the tyre, and it was firm. The axle nut had backed off half a turn. One washer was gone. Under the load the wheel had room to walk on the axle. Empty, it had looked true. I tightened the nut with a wet hand and finished the run. The next bag I looked for the washer first.
A barrow wheel turns on an axle. Nuts and washers keep the hub on that axle so the wheel stays in one plane. If a nut walks, the wheel wobbles. If a washer is missing, the nut has nothing to bear on and walks faster. People blame the tyre. A barrow that will not roll is usually the tyre is the flat, the split, the rim on the slab. This is the wheel that still turns and will not stay straight. Check the nut before you buy a tube.
When I check a wobble I tip the barrow and look at both ends of the axle. I want a nut that is tight, a washer under it, and no daylight where the hub should sit. I spin the wheel. A slow weave with a firm tyre is the nut or a bent axle. A wheel that will not spin is the tyre or a seized hub. I try the nut first. If it turns with my fingers, that was the job. I put the washer back if I still have it. A nyloc or a second locknut helps. A plain nut on a greasy thread will walk by the next load.
I also look at the fork. If one arm is bent, no nut will hold the wheel true. That is a knock from a slab edge, or from a path that has gone. Gravel that sinks is usually the base is why a barrow weaves on a rutted run even when the nut is tight. I still check the nut. Then I look at the path. I would not keep topping gravel while the wheel is loose. You spill the bag you meant to use.
A film of oil on the axle after you have tightened the nut is the same winter habit I wrote about in Winter tools need a wipe and a film of oil. Oil the axle, not the thread you need to stay put. A wet nut rusts to the axle and then you cannot service it. A greasy nut undoes itself in a week. Wipe the thread, tighten, then a drop on the spinning part.
A shed hook that actually holds a fork is for the tools. The barrow stays on its wheel in the shed. I do not leave that wheel in a puddle by the door. The nut rusts, the washer pits, and the first spring load wobbles. I check the nut when I hang the fork, not when the pan is full.
Skip a wheel held by one thin nut and no washer. Skip spinning the nut on with your fingers and calling it done. It will walk. Skip blaming the tyre because the barrow feels heavy. Squeeze the tyre. If it is firm, look at the axle. Skip a replacement wheel whose axle is a different diameter. The nuts will not seat and you have built a worse wobble. Skip loading the pan to test a nut you have just done up. Test it empty, then take a light load, then the gravel.
This shows in autumn, when the heavy jobs come back, gravel and wet stems and the compost bay. It shows in spring if the barrow sat all winter with a loose nut you never looked at. I now spin the wheel once before I fill the pan. If it weaves, I get the spanner, not another bag.
I do not need a new barrow because the wheel wobbled. I need a nut that stays, a washer under it, and a tyre I have already checked.
If I later add a buy link here, it will be a paid promo.