O-let welds are essentially a combination of a butt weld and a fillet weld. They are  most often overwelded far in excess of what is necessary. And for good reason. To really know what is required you need to call the O-let manufacturer and determine from them what the calculated nominal wall thickness is of the O-let in question. The problem is, each manufacturer calculates and forges them differently. So your data proliferates to the extreme, and is manufacturer sensitive.
So what most people do is just weld out past the 'bevel' that has been forged and/or machined into the fitting and then add a whoppin fillet, creating this 'knot-on-a-pyramid' appearance that most people agree is adequate.
This works very well for most O-lets, say 1/2" to even 6" or 8".
Its when O-lets in the range of say 24" are used on thinner wall pipes (horseshoeing your header), or when the O-let nominal size is the same as the header (I've seen inspecotrs insist so vehemently onthe 'pyramid' look that the weld ended up wrapping halfwya around the pipe), that the "pyramid" philosphy really breaks down. Or when welding stainless O-lets when you wish to reduce distortion.

In the absence of asking the manufacturer what their welding requirements are, the piping codes general require a complete joint penetration groove weld plus a reinforcing fillet weld. The size of the reinforcing fillet weld is dependent on the specific piping code, not the operating pressure.

One manufacturer that I have spoken with, will not warrantee their product unless the groove weld is a full sized complete joint penetration weld and they insist on a reinforcing fillet weld all around the fitting. Different fittings are used for different applications, i.e., pressure and other operating considerations.

Many of the integrally reinforced branch fitting I have seen in the field were not welded in accordance with the appropriate piping code and they did not meet the requirements of the manufacturer.

There are alternatives to using the integrally reinforced branch fitting (and the accompanying welds). They require some effort on the part of the design engineer to properly size the branch fitting and the reinforcement ring (if required). However, there may be an opportunity to reduce the distortion in the run pipe by minimizing the weld size requirements through design.

The intent of the integrally reinforced branch fitting is to reduce the engineering time required to design each branch connection by utilizing standardized fittings that have been designed and tested by the manufacturer. The integrally reinforced branch fitting (with full welds) eliminates the need to design (and install) reinforcing rings around the branch fitting to compensate for the volume of base metal (in the run pipe) removed to accommodate the branch.

Branch fittings that are not welded as per the manufacturer's requirements are not going to perform as they were intended. Groove welds that are not welded to completion can act as notched stress risers. What is often over looked are the stresses induced as the run pipe moves longitudinally due to changes in temperature. Those longitudinal movements induce bending loads on the branch fitting. Fatigue and cracking can result at stresses much lower than yield.

No insult is intended when I say that there are very few welders that have the training needed to perform the calculations necessary to design a branch connection in the field.  However, I've had welders say that the full weld isn't required because the system isn't operating at full pressure. The same welders lose the ability to speak when they are asked what piping code is specified. They get glassy eyed when they are asked what operating temperatures, pressures, and allowable unit stresses are permitted by the applicable piping code. The glassy eyed look becomes the 1000 yard stare when they are asked "what is the magnitude of the bending forces on the branch fitting due to thermal cycling?" Contrary to the belief held by many pipe welders, few welders are qualified to make those determinations.

My advice is to contact the design professional and the manufacturer if there is a question about the welding requirements for a particular fitting and application