Don't go mad trying for 1% repeatability. It's not necessary. And remember that the barrel also deflects under its own weight.
1) So the rifle should be supported in the same way as when it is fired. I.e. with a) the receiver clamped in a vice, and b) the fore-end wood resting on a support at the same place as the shooter's hand would be. If you omit b) the weight required will be considerably lower, leading to false conclusions.
2) The muzzle end needs to be hanging over the side of the bench or table, so that you can hang a weight on it.
3) if the rifle has a front barrel band, remove it. Otherwise the rest will be impossible.
4) Pull the barrel up (or press the wood down) so that you can slip in a piece of thin paper (cigarette paper) between the muzzle and the wood. Let it go, and you now have a piece of thin paper clamped between muzzle and wood by the upwards force we are trying to measure.
4) The tricky bit. Hang a weight on the muzzle end of the wood, underneath the point where the barrel bears on the wood. Increase the weight, piece by piece, until you can just slide out the paper. As the paper will have some friction against the wood (less against the metal) and the gap has to be opened a bit to enable the paper to slip out, the weight you have applied will be a touch more than the upward bearing force. But close enough for our purposes. Do it several times, to get a good feel for the slipping point.
5) OK, so I wrote glibly "Hang a weight...", inviting the question "How?". There, I am afraid, your DIY skills are required to make up an open loop of thick wire or maybe metal strip that you can hook onto the wood from below, and hang the weight(s) onto the loop. For such games I use a little plastic bucket with a loop handle that was a catering-sized mustard pot, and add lead bullets as required. Whatever you use, do not forget to weigh the support loop + bucket arrangement, as it is also part of the weight you are hanging onto the wood!
The above is not quite NPL-standards measurement, but for evaluating and adjusting old bangers, it is good enough!
P.S. The top of the wire loop in 5) must either be twisted together or restrained by a light clamp in order to prevent the loop opening up under load and slipping off - scratching the wood in the process!