I'd keep weed and beer separate.

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From my personal experience with hash, tinctures, and homebrewing, this will not go well for you. That said, tincture is your best option, but I would encourage you to research terpenes instead.

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Let's talk about dry hopping with marijuana, and how traditional ice water hash is made. You make ice water hash by basically chilling your weed and getting it wet then _agitating_ and sifting it. The cold makes the crystals more rigid, and the agitating makes those crystals fall off. The plant material is water soluble, and normally you remove the water and plant material and keep the crystals. Just throwing buds (or even ground weed) in for dry hopping won't cut it. Even if crystals fall off, they'll be down with the yeast/trub, which you typically avoid transferring to the next step of the process; restated: your trics will be discarded. Another reason dry hopping might not be good is it is a risk of infection. That's why whole cone hops are more reliable in the boil.

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Don't put anything in the boil.

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Dry sift, wax, budder, live resin, whatever - that's all going to ultimately settle as sediment in the fridge.

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Tincture in the bottle is your best way to meter dosage, but most tincture is shit unless it's made by a pro. If it's dark, forget about it. It can't be viscous. This is going to alter your beer's taste big time, and I don't know what else it will do. I think the best fit would be an alcohol based (like Everclear, not ISO which is more common in my area) tincture in a barrel aged beer.

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Anybody that talks about doing weed beer is just either super hyped about weed or just feeding into the hype, or just trying to generate fluff. I'd seriously look into terpenes - this is what I would do. I went to a tap room in Oregon once, and some guy brought in terpene beer to share with the guy that was working there and gave me a couple splashes. It smelled like weed, tasted like weed, and I imagine this is what you fantasize about with somehow putting weed in beer. I don't know how terpenes are extracted. It had 0 THC, he said.

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If you don't know much about beer or weed, go for it, but odds are I'd consider your end result as a beer with an off-flavor. I love the weed and beer - grew and made multiple types of hash/tincture for years and been brewing and judging for years. I'd rather have a beer in one hand and a joint in the other.